3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
286 C<isl> is released under the MIT license.
290 Permission is hereby granted, free of charge, to any person obtaining a copy of
291 this software and associated documentation files (the "Software"), to deal in
292 the Software without restriction, including without limitation the rights to
293 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
294 of the Software, and to permit persons to whom the Software is furnished to do
295 so, subject to the following conditions:
297 The above copyright notice and this permission notice shall be included in all
298 copies or substantial portions of the Software.
300 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
301 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
302 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
303 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
304 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
305 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
310 Note that by default C<isl> requires C<GMP>, which is released
311 under the GNU Lesser General Public License (LGPL). This means
312 that code linked against C<isl> is also linked against LGPL code.
314 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
315 will link against C<imath>, a library for exact integer arithmetic released
316 under the MIT license.
320 The source of C<isl> can be obtained either as a tarball
321 or from the git repository. Both are available from
322 L<http://isl.gforge.inria.fr/>.
323 The installation process depends on how you obtained
326 =head2 Installation from the git repository
330 =item 1 Clone or update the repository
332 The first time the source is obtained, you need to clone
335 git clone git://repo.or.cz/isl.git
337 To obtain updates, you need to pull in the latest changes
341 =item 2 Optionally get C<imath> submodule
343 To build C<isl> with C<imath>, you need to obtain the C<imath>
344 submodule by running in the git source tree of C<isl>
349 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
351 =item 2 Generate C<configure>
357 After performing the above steps, continue
358 with the L<Common installation instructions>.
360 =head2 Common installation instructions
364 =item 1 Obtain C<GMP>
366 By default, building C<isl> requires C<GMP>, including its headers files.
367 Your distribution may not provide these header files by default
368 and you may need to install a package called C<gmp-devel> or something
369 similar. Alternatively, C<GMP> can be built from
370 source, available from L<http://gmplib.org/>.
371 C<GMP> is not needed if you build C<isl> with C<imath>.
375 C<isl> uses the standard C<autoconf> C<configure> script.
380 optionally followed by some configure options.
381 A complete list of options can be obtained by running
385 Below we discuss some of the more common options.
391 Installation prefix for C<isl>
393 =item C<--with-int=[gmp|imath|imath-32]>
395 Select the integer library to be used by C<isl>, the default is C<gmp>.
396 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
397 for values out of the 32 bit range. In most applications, C<isl> will run
398 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
401 =item C<--with-gmp-prefix>
403 Installation prefix for C<GMP> (architecture-independent files).
405 =item C<--with-gmp-exec-prefix>
407 Installation prefix for C<GMP> (architecture-dependent files).
415 =item 4 Install (optional)
421 =head1 Integer Set Library
423 =head2 Memory Management
425 Since a high-level operation on isl objects usually involves
426 several substeps and since the user is usually not interested in
427 the intermediate results, most functions that return a new object
428 will also release all the objects passed as arguments.
429 If the user still wants to use one or more of these arguments
430 after the function call, she should pass along a copy of the
431 object rather than the object itself.
432 The user is then responsible for making sure that the original
433 object gets used somewhere else or is explicitly freed.
435 The arguments and return values of all documented functions are
436 annotated to make clear which arguments are released and which
437 arguments are preserved. In particular, the following annotations
444 C<__isl_give> means that a new object is returned.
445 The user should make sure that the returned pointer is
446 used exactly once as a value for an C<__isl_take> argument.
447 In between, it can be used as a value for as many
448 C<__isl_keep> arguments as the user likes.
449 There is one exception, and that is the case where the
450 pointer returned is C<NULL>. Is this case, the user
451 is free to use it as an C<__isl_take> argument or not.
452 When applied to a C<char *>, the returned pointer needs to be
457 C<__isl_null> means that a C<NULL> value is returned.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
479 This annotation may also be used on return values of
480 type C<const char *>, in which case the returned pointer should
481 not be freed by the user and is only valid until the object
482 from which it was derived is updated or freed.
486 =head2 Initialization
488 All manipulations of integer sets and relations occur within
489 the context of an C<isl_ctx>.
490 A given C<isl_ctx> can only be used within a single thread.
491 All arguments of a function are required to have been allocated
492 within the same context.
493 There are currently no functions available for moving an object
494 from one C<isl_ctx> to another C<isl_ctx>. This means that
495 there is currently no way of safely moving an object from one
496 thread to another, unless the whole C<isl_ctx> is moved.
498 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
499 freed using C<isl_ctx_free>.
500 All objects allocated within an C<isl_ctx> should be freed
501 before the C<isl_ctx> itself is freed.
503 isl_ctx *isl_ctx_alloc();
504 void isl_ctx_free(isl_ctx *ctx);
506 The user can impose a bound on the number of low-level I<operations>
507 that can be performed by an C<isl_ctx>. This bound can be set and
508 retrieved using the following functions. A bound of zero means that
509 no bound is imposed. The number of operations performed can be
510 reset using C<isl_ctx_reset_operations>. Note that the number
511 of low-level operations needed to perform a high-level computation
512 may differ significantly across different versions
513 of C<isl>, but it should be the same across different platforms
514 for the same version of C<isl>.
516 Warning: This feature is experimental. C<isl> has good support to abort and
517 bail out during the computation, but this feature may exercise error code paths
518 that are normally not used that much. Consequently, it is not unlikely that
519 hidden bugs will be exposed.
521 void isl_ctx_set_max_operations(isl_ctx *ctx,
522 unsigned long max_operations);
523 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
524 void isl_ctx_reset_operations(isl_ctx *ctx);
526 In order to be able to create an object in the same context
527 as another object, most object types (described later in
528 this document) provide a function to obtain the context
529 in which the object was created.
532 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
533 isl_ctx *isl_multi_val_get_ctx(
534 __isl_keep isl_multi_val *mv);
537 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
539 #include <isl/local_space.h>
540 isl_ctx *isl_local_space_get_ctx(
541 __isl_keep isl_local_space *ls);
544 isl_ctx *isl_set_list_get_ctx(
545 __isl_keep isl_set_list *list);
548 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
549 isl_ctx *isl_multi_aff_get_ctx(
550 __isl_keep isl_multi_aff *maff);
551 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
552 isl_ctx *isl_pw_multi_aff_get_ctx(
553 __isl_keep isl_pw_multi_aff *pma);
554 isl_ctx *isl_multi_pw_aff_get_ctx(
555 __isl_keep isl_multi_pw_aff *mpa);
556 isl_ctx *isl_union_pw_aff_get_ctx(
557 __isl_keep isl_union_pw_aff *upa);
558 isl_ctx *isl_union_pw_multi_aff_get_ctx(
559 __isl_keep isl_union_pw_multi_aff *upma);
560 isl_ctx *isl_multi_union_pw_aff_get_ctx(
561 __isl_keep isl_multi_union_pw_aff *mupa);
563 #include <isl/id_to_ast_expr.h>
564 isl_ctx *isl_id_to_ast_expr_get_ctx(
565 __isl_keep isl_id_to_ast_expr *id2expr);
567 #include <isl/point.h>
568 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
571 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
574 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
576 #include <isl/vertices.h>
577 isl_ctx *isl_vertices_get_ctx(
578 __isl_keep isl_vertices *vertices);
579 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
580 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
582 #include <isl/flow.h>
583 isl_ctx *isl_restriction_get_ctx(
584 __isl_keep isl_restriction *restr);
585 isl_ctx *isl_union_access_info_get_ctx(
586 __isl_keep isl_union_access_info *access);
587 isl_ctx *isl_union_flow_get_ctx(
588 __isl_keep isl_union_flow *flow);
590 #include <isl/schedule.h>
591 isl_ctx *isl_schedule_get_ctx(
592 __isl_keep isl_schedule *sched);
593 isl_ctx *isl_schedule_constraints_get_ctx(
594 __isl_keep isl_schedule_constraints *sc);
596 #include <isl/schedule_node.h>
597 isl_ctx *isl_schedule_node_get_ctx(
598 __isl_keep isl_schedule_node *node);
600 #include <isl/ast_build.h>
601 isl_ctx *isl_ast_build_get_ctx(
602 __isl_keep isl_ast_build *build);
605 isl_ctx *isl_ast_expr_get_ctx(
606 __isl_keep isl_ast_expr *expr);
607 isl_ctx *isl_ast_node_get_ctx(
608 __isl_keep isl_ast_node *node);
612 C<isl> uses two special return types for functions that either return
613 a boolean or that in principle do not return anything.
614 In particular, the C<isl_bool> type has three possible values:
615 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
616 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
617 C<isl_bool_error> (a negative integer value), indicating that something
618 went wrong. The following function can be used to negate an C<isl_bool>,
619 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
622 isl_bool isl_bool_not(isl_bool b);
624 The C<isl_stat> type has two possible values:
625 C<isl_stat_ok> (the integer value zero), indicating a successful
627 C<isl_stat_error> (a negative integer value), indicating that something
629 See L</"Error Handling"> for more information on
630 C<isl_bool_error> and C<isl_stat_error>.
634 An C<isl_val> represents an integer value, a rational value
635 or one of three special values, infinity, negative infinity and NaN.
636 Some predefined values can be created using the following functions.
639 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
640 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
641 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
642 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
643 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
644 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
646 Specific integer values can be created using the following functions.
649 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
651 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
653 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
654 size_t n, size_t size, const void *chunks);
656 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
657 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
658 The least significant digit is assumed to be stored first.
660 Value objects can be copied and freed using the following functions.
663 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
664 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
666 They can be inspected using the following functions.
669 long isl_val_get_num_si(__isl_keep isl_val *v);
670 long isl_val_get_den_si(__isl_keep isl_val *v);
671 __isl_give isl_val *isl_val_get_den_val(
672 __isl_keep isl_val *v);
673 double isl_val_get_d(__isl_keep isl_val *v);
674 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
676 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
677 size_t size, void *chunks);
679 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
680 of C<size> bytes needed to store the absolute value of the
682 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
683 which is assumed to have been preallocated by the caller.
684 The least significant digit is stored first.
685 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
686 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
687 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
689 An C<isl_val> can be modified using the following function.
692 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
695 The following unary properties are defined on C<isl_val>s.
698 int isl_val_sgn(__isl_keep isl_val *v);
699 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
700 isl_bool isl_val_is_one(__isl_keep isl_val *v);
701 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
702 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
703 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
704 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
705 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
706 isl_bool isl_val_is_int(__isl_keep isl_val *v);
707 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
708 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
709 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
710 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
712 Note that the sign of NaN is undefined.
714 The following binary properties are defined on pairs of C<isl_val>s.
717 isl_bool isl_val_lt(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_le(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_gt(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
723 isl_bool isl_val_ge(__isl_keep isl_val *v1,
724 __isl_keep isl_val *v2);
725 isl_bool isl_val_eq(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_ne(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
732 Comparisons to NaN always return false.
733 That is, a NaN is not considered to hold any relative position
734 with respect to any value. In particular, a NaN
735 is neither considered to be equal to nor to be different from
736 any value (including another NaN).
737 The function C<isl_val_abs_eq> checks whether its two arguments
738 are equal in absolute value.
740 For integer C<isl_val>s we additionally have the following binary property.
743 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
744 __isl_keep isl_val *v2);
746 An C<isl_val> can also be compared to an integer using the following
747 functions. The result of C<isl_val_cmp_si> undefined for NaN.
750 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
751 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
753 The following unary operations are available on C<isl_val>s.
756 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
757 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
758 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
759 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
760 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
761 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
762 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
764 The following binary operations are available on C<isl_val>s.
767 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
768 __isl_take isl_val *v2);
769 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
771 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
772 __isl_take isl_val *v2);
773 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
775 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
776 __isl_take isl_val *v2);
777 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
779 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
780 __isl_take isl_val *v2);
781 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
783 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
784 __isl_take isl_val *v2);
785 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
788 On integer values, we additionally have the following operations.
791 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
792 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
793 __isl_take isl_val *v2);
794 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
795 __isl_take isl_val *v2);
796 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
797 __isl_take isl_val *v2, __isl_give isl_val **x,
798 __isl_give isl_val **y);
800 The function C<isl_val_gcdext> returns the greatest common divisor g
801 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
802 that C<*x> * C<v1> + C<*y> * C<v2> = g.
804 =head3 GMP specific functions
806 These functions are only available if C<isl> has been compiled with C<GMP>
809 Specific integer and rational values can be created from C<GMP> values using
810 the following functions.
812 #include <isl/val_gmp.h>
813 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
815 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
816 const mpz_t n, const mpz_t d);
818 The numerator and denominator of a rational value can be extracted as
819 C<GMP> values using the following functions.
821 #include <isl/val_gmp.h>
822 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
823 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
825 =head2 Sets and Relations
827 C<isl> uses six types of objects for representing sets and relations,
828 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
829 C<isl_union_set> and C<isl_union_map>.
830 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
831 can be described as a conjunction of affine constraints, while
832 C<isl_set> and C<isl_map> represent unions of
833 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
834 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
835 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
836 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
837 where spaces are considered different if they have a different number
838 of dimensions and/or different names (see L<"Spaces">).
839 The difference between sets and relations (maps) is that sets have
840 one set of variables, while relations have two sets of variables,
841 input variables and output variables.
843 =head2 Error Handling
845 C<isl> supports different ways to react in case a runtime error is triggered.
846 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
847 with two maps that have incompatible spaces. There are three possible ways
848 to react on error: to warn, to continue or to abort.
850 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
851 the last error in the corresponding C<isl_ctx> and the function in which the
852 error was triggered returns a value indicating that some error has
853 occurred. In case of functions returning a pointer, this value is
854 C<NULL>. In case of functions returning an C<isl_bool> or an
855 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
856 An error does not corrupt internal state,
857 such that isl can continue to be used. C<isl> also provides functions to
858 read the last error, including the specific error message,
859 the isl source file where the error occurred and the line number,
860 and to reset all information about the last error. The
861 last error is only stored for information purposes. Its presence does not
862 change the behavior of C<isl>. Hence, resetting an error is not required to
863 continue to use isl, but only to observe new errors.
866 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
867 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
868 const char *isl_ctx_last_error_file(isl_ctx *ctx);
869 int isl_ctx_last_error_line(isl_ctx *ctx);
870 void isl_ctx_reset_error(isl_ctx *ctx);
872 If no error has occurred since the last call to C<isl_ctx_reset_error>,
873 then the functions C<isl_ctx_last_error_msg> and
874 C<isl_ctx_last_error_file> return C<NULL>.
876 Another option is to continue on error. This is similar to warn on error mode,
877 except that C<isl> does not print any warning. This allows a program to
878 implement its own error reporting.
880 The last option is to directly abort the execution of the program from within
881 the isl library. This makes it obviously impossible to recover from an error,
882 but it allows to directly spot the error location. By aborting on error,
883 debuggers break at the location the error occurred and can provide a stack
884 trace. Other tools that automatically provide stack traces on abort or that do
885 not want to continue execution after an error was triggered may also prefer to
888 The on error behavior of isl can be specified by calling
889 C<isl_options_set_on_error> or by setting the command line option
890 C<--isl-on-error>. Valid arguments for the function call are
891 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
892 choices for the command line option are C<warn>, C<continue> and C<abort>.
893 It is also possible to query the current error mode.
895 #include <isl/options.h>
896 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
897 int isl_options_get_on_error(isl_ctx *ctx);
901 Identifiers are used to identify both individual dimensions
902 and tuples of dimensions. They consist of an optional name and an optional
903 user pointer. The name and the user pointer cannot both be C<NULL>, however.
904 Identifiers with the same name but different pointer values
905 are considered to be distinct.
906 Similarly, identifiers with different names but the same pointer value
907 are also considered to be distinct.
908 Equal identifiers are represented using the same object.
909 Pairs of identifiers can therefore be tested for equality using the
911 Identifiers can be constructed, copied, freed, inspected and printed
912 using the following functions.
915 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
916 __isl_keep const char *name, void *user);
917 __isl_give isl_id *isl_id_set_free_user(
918 __isl_take isl_id *id,
919 void (*free_user)(void *user));
920 __isl_give isl_id *isl_id_copy(isl_id *id);
921 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
923 void *isl_id_get_user(__isl_keep isl_id *id);
924 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
926 __isl_give isl_printer *isl_printer_print_id(
927 __isl_take isl_printer *p, __isl_keep isl_id *id);
929 The callback set by C<isl_id_set_free_user> is called on the user
930 pointer when the last reference to the C<isl_id> is freed.
931 Note that C<isl_id_get_name> returns a pointer to some internal
932 data structure, so the result can only be used while the
933 corresponding C<isl_id> is alive.
937 Whenever a new set, relation or similar object is created from scratch,
938 the space in which it lives needs to be specified using an C<isl_space>.
939 Each space involves zero or more parameters and zero, one or two
940 tuples of set or input/output dimensions. The parameters and dimensions
941 are identified by an C<isl_dim_type> and a position.
942 The type C<isl_dim_param> refers to parameters,
943 the type C<isl_dim_set> refers to set dimensions (for spaces
944 with a single tuple of dimensions) and the types C<isl_dim_in>
945 and C<isl_dim_out> refer to input and output dimensions
946 (for spaces with two tuples of dimensions).
947 Local spaces (see L</"Local Spaces">) also contain dimensions
948 of type C<isl_dim_div>.
949 Note that parameters are only identified by their position within
950 a given object. Across different objects, parameters are (usually)
951 identified by their names or identifiers. Only unnamed parameters
952 are identified by their positions across objects. The use of unnamed
953 parameters is discouraged.
955 #include <isl/space.h>
956 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
957 unsigned nparam, unsigned n_in, unsigned n_out);
958 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
960 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
961 unsigned nparam, unsigned dim);
962 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
963 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
965 The space used for creating a parameter domain
966 needs to be created using C<isl_space_params_alloc>.
967 For other sets, the space
968 needs to be created using C<isl_space_set_alloc>, while
969 for a relation, the space
970 needs to be created using C<isl_space_alloc>.
972 To check whether a given space is that of a set or a map
973 or whether it is a parameter space, use these functions:
975 #include <isl/space.h>
976 isl_bool isl_space_is_params(__isl_keep isl_space *space);
977 isl_bool isl_space_is_set(__isl_keep isl_space *space);
978 isl_bool isl_space_is_map(__isl_keep isl_space *space);
980 Spaces can be compared using the following functions:
982 #include <isl/space.h>
983 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
984 __isl_keep isl_space *space2);
985 isl_bool isl_space_has_equal_params(
986 __isl_keep isl_space *space1,
987 __isl_keep isl_space *space2);
988 isl_bool isl_space_has_equal_tuples(
989 __isl_keep isl_space *space1,
990 __isl_keep isl_space *space2);
991 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
992 __isl_keep isl_space *space2);
993 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
994 __isl_keep isl_space *space2);
995 isl_bool isl_space_tuple_is_equal(
996 __isl_keep isl_space *space1,
997 enum isl_dim_type type1,
998 __isl_keep isl_space *space2,
999 enum isl_dim_type type2);
1001 C<isl_space_is_domain> checks whether the first argument is equal
1002 to the domain of the second argument. This requires in particular that
1003 the first argument is a set space and that the second argument
1004 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1005 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1006 spaces are the same. That is, it checks if they have the same
1007 identifier (if any), the same dimension and the same internal structure
1010 C<isl_space_has_equal_params> checks whether two spaces
1011 have the same parameters in the same order.
1012 C<isl_space_has_equal_tuples> check whether two spaces have
1013 the same tuples. In contrast to C<isl_space_is_equal> below,
1014 it does not check the
1015 parameters. This is useful because many C<isl> functions align the
1016 parameters before they perform their operations, such that equivalence
1018 C<isl_space_is_equal> checks whether two spaces are identical,
1019 meaning that they have the same parameters and the same tuples.
1020 That is, it checks whether both C<isl_space_has_equal_params> and
1021 C<isl_space_has_equal_tuples> hold.
1023 It is often useful to create objects that live in the
1024 same space as some other object. This can be accomplished
1025 by creating the new objects
1026 (see L</"Creating New Sets and Relations"> or
1027 L</"Functions">) based on the space
1028 of the original object.
1030 #include <isl/set.h>
1031 __isl_give isl_space *isl_basic_set_get_space(
1032 __isl_keep isl_basic_set *bset);
1033 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1035 #include <isl/union_set.h>
1036 __isl_give isl_space *isl_union_set_get_space(
1037 __isl_keep isl_union_set *uset);
1039 #include <isl/map.h>
1040 __isl_give isl_space *isl_basic_map_get_space(
1041 __isl_keep isl_basic_map *bmap);
1042 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1044 #include <isl/union_map.h>
1045 __isl_give isl_space *isl_union_map_get_space(
1046 __isl_keep isl_union_map *umap);
1048 #include <isl/constraint.h>
1049 __isl_give isl_space *isl_constraint_get_space(
1050 __isl_keep isl_constraint *constraint);
1052 #include <isl/polynomial.h>
1053 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1054 __isl_keep isl_qpolynomial *qp);
1055 __isl_give isl_space *isl_qpolynomial_get_space(
1056 __isl_keep isl_qpolynomial *qp);
1057 __isl_give isl_space *
1058 isl_qpolynomial_fold_get_domain_space(
1059 __isl_keep isl_qpolynomial_fold *fold);
1060 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1061 __isl_keep isl_qpolynomial_fold *fold);
1062 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1063 __isl_keep isl_pw_qpolynomial *pwqp);
1064 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1065 __isl_keep isl_pw_qpolynomial *pwqp);
1066 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1067 __isl_keep isl_pw_qpolynomial_fold *pwf);
1068 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1069 __isl_keep isl_pw_qpolynomial_fold *pwf);
1070 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1071 __isl_keep isl_union_pw_qpolynomial *upwqp);
1072 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1073 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1075 #include <isl/val.h>
1076 __isl_give isl_space *isl_multi_val_get_space(
1077 __isl_keep isl_multi_val *mv);
1079 #include <isl/aff.h>
1080 __isl_give isl_space *isl_aff_get_domain_space(
1081 __isl_keep isl_aff *aff);
1082 __isl_give isl_space *isl_aff_get_space(
1083 __isl_keep isl_aff *aff);
1084 __isl_give isl_space *isl_pw_aff_get_domain_space(
1085 __isl_keep isl_pw_aff *pwaff);
1086 __isl_give isl_space *isl_pw_aff_get_space(
1087 __isl_keep isl_pw_aff *pwaff);
1088 __isl_give isl_space *isl_multi_aff_get_domain_space(
1089 __isl_keep isl_multi_aff *maff);
1090 __isl_give isl_space *isl_multi_aff_get_space(
1091 __isl_keep isl_multi_aff *maff);
1092 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1093 __isl_keep isl_pw_multi_aff *pma);
1094 __isl_give isl_space *isl_pw_multi_aff_get_space(
1095 __isl_keep isl_pw_multi_aff *pma);
1096 __isl_give isl_space *isl_union_pw_aff_get_space(
1097 __isl_keep isl_union_pw_aff *upa);
1098 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1099 __isl_keep isl_union_pw_multi_aff *upma);
1100 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1101 __isl_keep isl_multi_pw_aff *mpa);
1102 __isl_give isl_space *isl_multi_pw_aff_get_space(
1103 __isl_keep isl_multi_pw_aff *mpa);
1104 __isl_give isl_space *
1105 isl_multi_union_pw_aff_get_domain_space(
1106 __isl_keep isl_multi_union_pw_aff *mupa);
1107 __isl_give isl_space *
1108 isl_multi_union_pw_aff_get_space(
1109 __isl_keep isl_multi_union_pw_aff *mupa);
1111 #include <isl/point.h>
1112 __isl_give isl_space *isl_point_get_space(
1113 __isl_keep isl_point *pnt);
1115 The number of dimensions of a given type of space
1116 may be read off from a space or an object that lives
1117 in a space using the following functions.
1118 In case of C<isl_space_dim>, type may be
1119 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1120 C<isl_dim_out> (only for relations), C<isl_dim_set>
1121 (only for sets) or C<isl_dim_all>.
1123 #include <isl/space.h>
1124 unsigned isl_space_dim(__isl_keep isl_space *space,
1125 enum isl_dim_type type);
1127 #include <isl/local_space.h>
1128 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1129 enum isl_dim_type type);
1131 #include <isl/set.h>
1132 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1133 enum isl_dim_type type);
1134 unsigned isl_set_dim(__isl_keep isl_set *set,
1135 enum isl_dim_type type);
1137 #include <isl/union_set.h>
1138 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1139 enum isl_dim_type type);
1141 #include <isl/map.h>
1142 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1143 enum isl_dim_type type);
1144 unsigned isl_map_dim(__isl_keep isl_map *map,
1145 enum isl_dim_type type);
1147 #include <isl/union_map.h>
1148 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1149 enum isl_dim_type type);
1151 #include <isl/val.h>
1152 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1153 enum isl_dim_type type);
1155 #include <isl/aff.h>
1156 int isl_aff_dim(__isl_keep isl_aff *aff,
1157 enum isl_dim_type type);
1158 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1159 enum isl_dim_type type);
1160 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1161 enum isl_dim_type type);
1162 unsigned isl_pw_multi_aff_dim(
1163 __isl_keep isl_pw_multi_aff *pma,
1164 enum isl_dim_type type);
1165 unsigned isl_multi_pw_aff_dim(
1166 __isl_keep isl_multi_pw_aff *mpa,
1167 enum isl_dim_type type);
1168 unsigned isl_union_pw_aff_dim(
1169 __isl_keep isl_union_pw_aff *upa,
1170 enum isl_dim_type type);
1171 unsigned isl_union_pw_multi_aff_dim(
1172 __isl_keep isl_union_pw_multi_aff *upma,
1173 enum isl_dim_type type);
1174 unsigned isl_multi_union_pw_aff_dim(
1175 __isl_keep isl_multi_union_pw_aff *mupa,
1176 enum isl_dim_type type);
1178 #include <isl/polynomial.h>
1179 unsigned isl_union_pw_qpolynomial_dim(
1180 __isl_keep isl_union_pw_qpolynomial *upwqp,
1181 enum isl_dim_type type);
1182 unsigned isl_union_pw_qpolynomial_fold_dim(
1183 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1184 enum isl_dim_type type);
1186 Note that an C<isl_union_set>, an C<isl_union_map>,
1187 an C<isl_union_pw_multi_aff>,
1188 an C<isl_union_pw_qpolynomial> and
1189 an C<isl_union_pw_qpolynomial_fold>
1190 only have parameters.
1192 Additional parameters can be added to a space using the following function.
1194 #include <isl/space.h>
1195 __isl_give isl_space *isl_space_add_param_id(
1196 __isl_take isl_space *space,
1197 __isl_take isl_id *id);
1199 If a parameter with the given identifier already appears in the space,
1200 then it is not added again.
1202 The identifiers or names of the individual dimensions of spaces
1203 may be set or read off using the following functions on spaces
1204 or objects that live in spaces.
1205 These functions are mostly useful to obtain the identifiers, positions
1206 or names of the parameters. Identifiers of individual dimensions are
1207 essentially only useful for printing. They are ignored by all other
1208 operations and may not be preserved across those operations.
1210 #include <isl/space.h>
1211 __isl_give isl_space *isl_space_set_dim_id(
1212 __isl_take isl_space *space,
1213 enum isl_dim_type type, unsigned pos,
1214 __isl_take isl_id *id);
1215 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1216 enum isl_dim_type type, unsigned pos);
1217 __isl_give isl_id *isl_space_get_dim_id(
1218 __isl_keep isl_space *space,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_space *isl_space_set_dim_name(
1221 __isl_take isl_space *space,
1222 enum isl_dim_type type, unsigned pos,
1223 __isl_keep const char *name);
1224 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_keep const char *isl_space_get_dim_name(
1227 __isl_keep isl_space *space,
1228 enum isl_dim_type type, unsigned pos);
1230 #include <isl/local_space.h>
1231 __isl_give isl_local_space *isl_local_space_set_dim_id(
1232 __isl_take isl_local_space *ls,
1233 enum isl_dim_type type, unsigned pos,
1234 __isl_take isl_id *id);
1235 isl_bool isl_local_space_has_dim_id(
1236 __isl_keep isl_local_space *ls,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_give isl_id *isl_local_space_get_dim_id(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, unsigned pos);
1241 __isl_give isl_local_space *isl_local_space_set_dim_name(
1242 __isl_take isl_local_space *ls,
1243 enum isl_dim_type type, unsigned pos, const char *s);
1244 isl_bool isl_local_space_has_dim_name(
1245 __isl_keep isl_local_space *ls,
1246 enum isl_dim_type type, unsigned pos)
1247 const char *isl_local_space_get_dim_name(
1248 __isl_keep isl_local_space *ls,
1249 enum isl_dim_type type, unsigned pos);
1251 #include <isl/constraint.h>
1252 const char *isl_constraint_get_dim_name(
1253 __isl_keep isl_constraint *constraint,
1254 enum isl_dim_type type, unsigned pos);
1256 #include <isl/set.h>
1257 __isl_give isl_id *isl_basic_set_get_dim_id(
1258 __isl_keep isl_basic_set *bset,
1259 enum isl_dim_type type, unsigned pos);
1260 __isl_give isl_set *isl_set_set_dim_id(
1261 __isl_take isl_set *set, enum isl_dim_type type,
1262 unsigned pos, __isl_take isl_id *id);
1263 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1264 enum isl_dim_type type, unsigned pos);
1265 __isl_give isl_id *isl_set_get_dim_id(
1266 __isl_keep isl_set *set, enum isl_dim_type type,
1268 const char *isl_basic_set_get_dim_name(
1269 __isl_keep isl_basic_set *bset,
1270 enum isl_dim_type type, unsigned pos);
1271 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1272 enum isl_dim_type type, unsigned pos);
1273 const char *isl_set_get_dim_name(
1274 __isl_keep isl_set *set,
1275 enum isl_dim_type type, unsigned pos);
1277 #include <isl/map.h>
1278 __isl_give isl_map *isl_map_set_dim_id(
1279 __isl_take isl_map *map, enum isl_dim_type type,
1280 unsigned pos, __isl_take isl_id *id);
1281 isl_bool isl_basic_map_has_dim_id(
1282 __isl_keep isl_basic_map *bmap,
1283 enum isl_dim_type type, unsigned pos);
1284 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1285 enum isl_dim_type type, unsigned pos);
1286 __isl_give isl_id *isl_map_get_dim_id(
1287 __isl_keep isl_map *map, enum isl_dim_type type,
1289 __isl_give isl_id *isl_union_map_get_dim_id(
1290 __isl_keep isl_union_map *umap,
1291 enum isl_dim_type type, unsigned pos);
1292 const char *isl_basic_map_get_dim_name(
1293 __isl_keep isl_basic_map *bmap,
1294 enum isl_dim_type type, unsigned pos);
1295 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1296 enum isl_dim_type type, unsigned pos);
1297 const char *isl_map_get_dim_name(
1298 __isl_keep isl_map *map,
1299 enum isl_dim_type type, unsigned pos);
1301 #include <isl/val.h>
1302 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1303 __isl_take isl_multi_val *mv,
1304 enum isl_dim_type type, unsigned pos,
1305 __isl_take isl_id *id);
1306 __isl_give isl_id *isl_multi_val_get_dim_id(
1307 __isl_keep isl_multi_val *mv,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1310 __isl_take isl_multi_val *mv,
1311 enum isl_dim_type type, unsigned pos, const char *s);
1313 #include <isl/aff.h>
1314 __isl_give isl_aff *isl_aff_set_dim_id(
1315 __isl_take isl_aff *aff, enum isl_dim_type type,
1316 unsigned pos, __isl_take isl_id *id);
1317 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1318 __isl_take isl_multi_aff *maff,
1319 enum isl_dim_type type, unsigned pos,
1320 __isl_take isl_id *id);
1321 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1322 __isl_take isl_pw_aff *pma,
1323 enum isl_dim_type type, unsigned pos,
1324 __isl_take isl_id *id);
1325 __isl_give isl_multi_pw_aff *
1326 isl_multi_pw_aff_set_dim_id(
1327 __isl_take isl_multi_pw_aff *mpa,
1328 enum isl_dim_type type, unsigned pos,
1329 __isl_take isl_id *id);
1330 __isl_give isl_multi_union_pw_aff *
1331 isl_multi_union_pw_aff_set_dim_id(
1332 __isl_take isl_multi_union_pw_aff *mupa,
1333 enum isl_dim_type type, unsigned pos,
1334 __isl_take isl_id *id);
1335 __isl_give isl_id *isl_multi_aff_get_dim_id(
1336 __isl_keep isl_multi_aff *ma,
1337 enum isl_dim_type type, unsigned pos);
1338 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_id *isl_pw_aff_get_dim_id(
1341 __isl_keep isl_pw_aff *pa,
1342 enum isl_dim_type type, unsigned pos);
1343 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1344 __isl_keep isl_pw_multi_aff *pma,
1345 enum isl_dim_type type, unsigned pos);
1346 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1347 __isl_keep isl_multi_pw_aff *mpa,
1348 enum isl_dim_type type, unsigned pos);
1349 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1350 __isl_keep isl_multi_union_pw_aff *mupa,
1351 enum isl_dim_type type, unsigned pos);
1352 __isl_give isl_aff *isl_aff_set_dim_name(
1353 __isl_take isl_aff *aff, enum isl_dim_type type,
1354 unsigned pos, const char *s);
1355 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1356 __isl_take isl_multi_aff *maff,
1357 enum isl_dim_type type, unsigned pos, const char *s);
1358 __isl_give isl_multi_pw_aff *
1359 isl_multi_pw_aff_set_dim_name(
1360 __isl_take isl_multi_pw_aff *mpa,
1361 enum isl_dim_type type, unsigned pos, const char *s);
1362 __isl_give isl_union_pw_aff *
1363 isl_union_pw_aff_set_dim_name(
1364 __isl_take isl_union_pw_aff *upa,
1365 enum isl_dim_type type, unsigned pos,
1367 __isl_give isl_union_pw_multi_aff *
1368 isl_union_pw_multi_aff_set_dim_name(
1369 __isl_take isl_union_pw_multi_aff *upma,
1370 enum isl_dim_type type, unsigned pos,
1372 __isl_give isl_multi_union_pw_aff *
1373 isl_multi_union_pw_aff_set_dim_name(
1374 __isl_take isl_multi_union_pw_aff *mupa,
1375 enum isl_dim_type type, unsigned pos,
1376 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1377 enum isl_dim_type type, unsigned pos);
1378 const char *isl_pw_aff_get_dim_name(
1379 __isl_keep isl_pw_aff *pa,
1380 enum isl_dim_type type, unsigned pos);
1381 const char *isl_pw_multi_aff_get_dim_name(
1382 __isl_keep isl_pw_multi_aff *pma,
1383 enum isl_dim_type type, unsigned pos);
1385 #include <isl/polynomial.h>
1386 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1387 __isl_take isl_qpolynomial *qp,
1388 enum isl_dim_type type, unsigned pos,
1390 __isl_give isl_pw_qpolynomial *
1391 isl_pw_qpolynomial_set_dim_name(
1392 __isl_take isl_pw_qpolynomial *pwqp,
1393 enum isl_dim_type type, unsigned pos,
1395 __isl_give isl_pw_qpolynomial_fold *
1396 isl_pw_qpolynomial_fold_set_dim_name(
1397 __isl_take isl_pw_qpolynomial_fold *pwf,
1398 enum isl_dim_type type, unsigned pos,
1400 __isl_give isl_union_pw_qpolynomial *
1401 isl_union_pw_qpolynomial_set_dim_name(
1402 __isl_take isl_union_pw_qpolynomial *upwqp,
1403 enum isl_dim_type type, unsigned pos,
1405 __isl_give isl_union_pw_qpolynomial_fold *
1406 isl_union_pw_qpolynomial_fold_set_dim_name(
1407 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1408 enum isl_dim_type type, unsigned pos,
1411 Note that C<isl_space_get_name> returns a pointer to some internal
1412 data structure, so the result can only be used while the
1413 corresponding C<isl_space> is alive.
1414 Also note that every function that operates on two sets or relations
1415 requires that both arguments have the same parameters. This also
1416 means that if one of the arguments has named parameters, then the
1417 other needs to have named parameters too and the names need to match.
1418 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1419 arguments may have different parameters (as long as they are named),
1420 in which case the result will have as parameters the union of the parameters of
1423 Given the identifier or name of a dimension (typically a parameter),
1424 its position can be obtained from the following functions.
1426 #include <isl/space.h>
1427 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1428 enum isl_dim_type type, __isl_keep isl_id *id);
1429 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1430 enum isl_dim_type type, const char *name);
1432 #include <isl/local_space.h>
1433 int isl_local_space_find_dim_by_name(
1434 __isl_keep isl_local_space *ls,
1435 enum isl_dim_type type, const char *name);
1437 #include <isl/val.h>
1438 int isl_multi_val_find_dim_by_id(
1439 __isl_keep isl_multi_val *mv,
1440 enum isl_dim_type type, __isl_keep isl_id *id);
1441 int isl_multi_val_find_dim_by_name(
1442 __isl_keep isl_multi_val *mv,
1443 enum isl_dim_type type, const char *name);
1445 #include <isl/set.h>
1446 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1447 enum isl_dim_type type, __isl_keep isl_id *id);
1448 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1449 enum isl_dim_type type, const char *name);
1451 #include <isl/map.h>
1452 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1453 enum isl_dim_type type, __isl_keep isl_id *id);
1454 int isl_basic_map_find_dim_by_name(
1455 __isl_keep isl_basic_map *bmap,
1456 enum isl_dim_type type, const char *name);
1457 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1458 enum isl_dim_type type, const char *name);
1459 int isl_union_map_find_dim_by_name(
1460 __isl_keep isl_union_map *umap,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/aff.h>
1464 int isl_multi_aff_find_dim_by_id(
1465 __isl_keep isl_multi_aff *ma,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_multi_pw_aff_find_dim_by_id(
1468 __isl_keep isl_multi_pw_aff *mpa,
1469 enum isl_dim_type type, __isl_keep isl_id *id);
1470 int isl_multi_union_pw_aff_find_dim_by_id(
1471 __isl_keep isl_union_multi_pw_aff *mupa,
1472 enum isl_dim_type type, __isl_keep isl_id *id);
1473 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1474 enum isl_dim_type type, const char *name);
1475 int isl_multi_aff_find_dim_by_name(
1476 __isl_keep isl_multi_aff *ma,
1477 enum isl_dim_type type, const char *name);
1478 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1479 enum isl_dim_type type, const char *name);
1480 int isl_multi_pw_aff_find_dim_by_name(
1481 __isl_keep isl_multi_pw_aff *mpa,
1482 enum isl_dim_type type, const char *name);
1483 int isl_pw_multi_aff_find_dim_by_name(
1484 __isl_keep isl_pw_multi_aff *pma,
1485 enum isl_dim_type type, const char *name);
1486 int isl_union_pw_aff_find_dim_by_name(
1487 __isl_keep isl_union_pw_aff *upa,
1488 enum isl_dim_type type, const char *name);
1489 int isl_union_pw_multi_aff_find_dim_by_name(
1490 __isl_keep isl_union_pw_multi_aff *upma,
1491 enum isl_dim_type type, const char *name);
1492 int isl_multi_union_pw_aff_find_dim_by_name(
1493 __isl_keep isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, const char *name);
1496 #include <isl/polynomial.h>
1497 int isl_pw_qpolynomial_find_dim_by_name(
1498 __isl_keep isl_pw_qpolynomial *pwqp,
1499 enum isl_dim_type type, const char *name);
1500 int isl_pw_qpolynomial_fold_find_dim_by_name(
1501 __isl_keep isl_pw_qpolynomial_fold *pwf,
1502 enum isl_dim_type type, const char *name);
1503 int isl_union_pw_qpolynomial_find_dim_by_name(
1504 __isl_keep isl_union_pw_qpolynomial *upwqp,
1505 enum isl_dim_type type, const char *name);
1506 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1507 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1508 enum isl_dim_type type, const char *name);
1510 The identifiers or names of entire spaces may be set or read off
1511 using the following functions.
1513 #include <isl/space.h>
1514 __isl_give isl_space *isl_space_set_tuple_id(
1515 __isl_take isl_space *space,
1516 enum isl_dim_type type, __isl_take isl_id *id);
1517 __isl_give isl_space *isl_space_reset_tuple_id(
1518 __isl_take isl_space *space, enum isl_dim_type type);
1519 isl_bool isl_space_has_tuple_id(
1520 __isl_keep isl_space *space,
1521 enum isl_dim_type type);
1522 __isl_give isl_id *isl_space_get_tuple_id(
1523 __isl_keep isl_space *space, enum isl_dim_type type);
1524 __isl_give isl_space *isl_space_set_tuple_name(
1525 __isl_take isl_space *space,
1526 enum isl_dim_type type, const char *s);
1527 isl_bool isl_space_has_tuple_name(
1528 __isl_keep isl_space *space,
1529 enum isl_dim_type type);
1530 __isl_keep const char *isl_space_get_tuple_name(
1531 __isl_keep isl_space *space,
1532 enum isl_dim_type type);
1534 #include <isl/local_space.h>
1535 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1536 __isl_take isl_local_space *ls,
1537 enum isl_dim_type type, __isl_take isl_id *id);
1539 #include <isl/set.h>
1540 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1541 __isl_take isl_basic_set *bset,
1542 __isl_take isl_id *id);
1543 __isl_give isl_set *isl_set_set_tuple_id(
1544 __isl_take isl_set *set, __isl_take isl_id *id);
1545 __isl_give isl_set *isl_set_reset_tuple_id(
1546 __isl_take isl_set *set);
1547 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1548 __isl_give isl_id *isl_set_get_tuple_id(
1549 __isl_keep isl_set *set);
1550 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1551 __isl_take isl_basic_set *set, const char *s);
1552 __isl_give isl_set *isl_set_set_tuple_name(
1553 __isl_take isl_set *set, const char *s);
1554 const char *isl_basic_set_get_tuple_name(
1555 __isl_keep isl_basic_set *bset);
1556 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1557 const char *isl_set_get_tuple_name(
1558 __isl_keep isl_set *set);
1560 #include <isl/map.h>
1561 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1562 __isl_take isl_basic_map *bmap,
1563 enum isl_dim_type type, __isl_take isl_id *id);
1564 __isl_give isl_map *isl_map_set_tuple_id(
1565 __isl_take isl_map *map, enum isl_dim_type type,
1566 __isl_take isl_id *id);
1567 __isl_give isl_map *isl_map_reset_tuple_id(
1568 __isl_take isl_map *map, enum isl_dim_type type);
1569 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1570 enum isl_dim_type type);
1571 __isl_give isl_id *isl_map_get_tuple_id(
1572 __isl_keep isl_map *map, enum isl_dim_type type);
1573 __isl_give isl_map *isl_map_set_tuple_name(
1574 __isl_take isl_map *map,
1575 enum isl_dim_type type, const char *s);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1583 enum isl_dim_type type);
1584 const char *isl_map_get_tuple_name(
1585 __isl_keep isl_map *map,
1586 enum isl_dim_type type);
1588 #include <isl/val.h>
1589 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1590 __isl_take isl_multi_val *mv,
1591 enum isl_dim_type type, __isl_take isl_id *id);
1592 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1593 __isl_take isl_multi_val *mv,
1594 enum isl_dim_type type);
1595 isl_bool isl_multi_val_has_tuple_id(
1596 __isl_keep isl_multi_val *mv,
1597 enum isl_dim_type type);
1598 __isl_give isl_id *isl_multi_val_get_tuple_id(
1599 __isl_keep isl_multi_val *mv,
1600 enum isl_dim_type type);
1601 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1602 __isl_take isl_multi_val *mv,
1603 enum isl_dim_type type, const char *s);
1604 const char *isl_multi_val_get_tuple_name(
1605 __isl_keep isl_multi_val *mv,
1606 enum isl_dim_type type);
1608 #include <isl/aff.h>
1609 __isl_give isl_aff *isl_aff_set_tuple_id(
1610 __isl_take isl_aff *aff,
1611 enum isl_dim_type type, __isl_take isl_id *id);
1612 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1613 __isl_take isl_multi_aff *maff,
1614 enum isl_dim_type type, __isl_take isl_id *id);
1615 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1616 __isl_take isl_pw_aff *pwaff,
1617 enum isl_dim_type type, __isl_take isl_id *id);
1618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1619 __isl_take isl_pw_multi_aff *pma,
1620 enum isl_dim_type type, __isl_take isl_id *id);
1621 __isl_give isl_multi_union_pw_aff *
1622 isl_multi_union_pw_aff_set_tuple_id(
1623 __isl_take isl_multi_union_pw_aff *mupa,
1624 enum isl_dim_type type, __isl_take isl_id *id);
1625 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1626 __isl_take isl_multi_aff *ma,
1627 enum isl_dim_type type);
1628 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1629 __isl_take isl_pw_aff *pa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_pw_aff *
1632 isl_multi_pw_aff_reset_tuple_id(
1633 __isl_take isl_multi_pw_aff *mpa,
1634 enum isl_dim_type type);
1635 __isl_give isl_pw_multi_aff *
1636 isl_pw_multi_aff_reset_tuple_id(
1637 __isl_take isl_pw_multi_aff *pma,
1638 enum isl_dim_type type);
1639 __isl_give isl_multi_union_pw_aff *
1640 isl_multi_union_pw_aff_reset_tuple_id(
1641 __isl_take isl_multi_union_pw_aff *mupa,
1642 enum isl_dim_type type);
1643 isl_bool isl_multi_aff_has_tuple_id(
1644 __isl_keep isl_multi_aff *ma,
1645 enum isl_dim_type type);
1646 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1647 __isl_keep isl_multi_aff *ma,
1648 enum isl_dim_type type);
1649 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1650 enum isl_dim_type type);
1651 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1652 __isl_keep isl_pw_aff *pa,
1653 enum isl_dim_type type);
1654 isl_bool isl_pw_multi_aff_has_tuple_id(
1655 __isl_keep isl_pw_multi_aff *pma,
1656 enum isl_dim_type type);
1657 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1658 __isl_keep isl_pw_multi_aff *pma,
1659 enum isl_dim_type type);
1660 isl_bool isl_multi_pw_aff_has_tuple_id(
1661 __isl_keep isl_multi_pw_aff *mpa,
1662 enum isl_dim_type type);
1663 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1664 __isl_keep isl_multi_pw_aff *mpa,
1665 enum isl_dim_type type);
1666 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1667 __isl_keep isl_multi_union_pw_aff *mupa,
1668 enum isl_dim_type type);
1669 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1670 __isl_keep isl_multi_union_pw_aff *mupa,
1671 enum isl_dim_type type);
1672 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1673 __isl_take isl_multi_aff *maff,
1674 enum isl_dim_type type, const char *s);
1675 __isl_give isl_multi_pw_aff *
1676 isl_multi_pw_aff_set_tuple_name(
1677 __isl_take isl_multi_pw_aff *mpa,
1678 enum isl_dim_type type, const char *s);
1679 __isl_give isl_multi_union_pw_aff *
1680 isl_multi_union_pw_aff_set_tuple_name(
1681 __isl_take isl_multi_union_pw_aff *mupa,
1682 enum isl_dim_type type, const char *s);
1683 const char *isl_multi_aff_get_tuple_name(
1684 __isl_keep isl_multi_aff *multi,
1685 enum isl_dim_type type);
1686 isl_bool isl_pw_multi_aff_has_tuple_name(
1687 __isl_keep isl_pw_multi_aff *pma,
1688 enum isl_dim_type type);
1689 const char *isl_pw_multi_aff_get_tuple_name(
1690 __isl_keep isl_pw_multi_aff *pma,
1691 enum isl_dim_type type);
1692 const char *isl_multi_union_pw_aff_get_tuple_name(
1693 __isl_keep isl_multi_union_pw_aff *mupa,
1694 enum isl_dim_type type);
1696 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1697 or C<isl_dim_set>. As with C<isl_space_get_name>,
1698 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1700 Binary operations require the corresponding spaces of their arguments
1701 to have the same name.
1703 To keep the names of all parameters and tuples, but reset the user pointers
1704 of all the corresponding identifiers, use the following function.
1706 #include <isl/space.h>
1707 __isl_give isl_space *isl_space_reset_user(
1708 __isl_take isl_space *space);
1710 #include <isl/set.h>
1711 __isl_give isl_set *isl_set_reset_user(
1712 __isl_take isl_set *set);
1714 #include <isl/map.h>
1715 __isl_give isl_map *isl_map_reset_user(
1716 __isl_take isl_map *map);
1718 #include <isl/union_set.h>
1719 __isl_give isl_union_set *isl_union_set_reset_user(
1720 __isl_take isl_union_set *uset);
1722 #include <isl/union_map.h>
1723 __isl_give isl_union_map *isl_union_map_reset_user(
1724 __isl_take isl_union_map *umap);
1726 #include <isl/val.h>
1727 __isl_give isl_multi_val *isl_multi_val_reset_user(
1728 __isl_take isl_multi_val *mv);
1730 #include <isl/aff.h>
1731 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1732 __isl_take isl_multi_aff *ma);
1733 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1734 __isl_take isl_pw_aff *pa);
1735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1736 __isl_take isl_multi_pw_aff *mpa);
1737 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1738 __isl_take isl_pw_multi_aff *pma);
1739 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1740 __isl_take isl_union_pw_aff *upa);
1741 __isl_give isl_multi_union_pw_aff *
1742 isl_multi_union_pw_aff_reset_user(
1743 __isl_take isl_multi_union_pw_aff *mupa);
1744 __isl_give isl_union_pw_multi_aff *
1745 isl_union_pw_multi_aff_reset_user(
1746 __isl_take isl_union_pw_multi_aff *upma);
1748 #include <isl/polynomial.h>
1749 __isl_give isl_pw_qpolynomial *
1750 isl_pw_qpolynomial_reset_user(
1751 __isl_take isl_pw_qpolynomial *pwqp);
1752 __isl_give isl_union_pw_qpolynomial *
1753 isl_union_pw_qpolynomial_reset_user(
1754 __isl_take isl_union_pw_qpolynomial *upwqp);
1755 __isl_give isl_pw_qpolynomial_fold *
1756 isl_pw_qpolynomial_fold_reset_user(
1757 __isl_take isl_pw_qpolynomial_fold *pwf);
1758 __isl_give isl_union_pw_qpolynomial_fold *
1759 isl_union_pw_qpolynomial_fold_reset_user(
1760 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1762 Spaces can be nested. In particular, the domain of a set or
1763 the domain or range of a relation can be a nested relation.
1764 This process is also called I<wrapping>.
1765 The functions for detecting, constructing and deconstructing
1766 such nested spaces can be found in the wrapping properties
1767 of L</"Unary Properties">, the wrapping operations
1768 of L</"Unary Operations"> and the Cartesian product operations
1769 of L</"Basic Operations">.
1771 Spaces can be created from other spaces
1772 using the functions described in L</"Unary Operations">
1773 and L</"Binary Operations">.
1777 A local space is essentially a space with
1778 zero or more existentially quantified variables.
1779 The local space of various objects can be obtained
1780 using the following functions.
1782 #include <isl/constraint.h>
1783 __isl_give isl_local_space *isl_constraint_get_local_space(
1784 __isl_keep isl_constraint *constraint);
1786 #include <isl/set.h>
1787 __isl_give isl_local_space *isl_basic_set_get_local_space(
1788 __isl_keep isl_basic_set *bset);
1790 #include <isl/map.h>
1791 __isl_give isl_local_space *isl_basic_map_get_local_space(
1792 __isl_keep isl_basic_map *bmap);
1794 #include <isl/aff.h>
1795 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1796 __isl_keep isl_aff *aff);
1797 __isl_give isl_local_space *isl_aff_get_local_space(
1798 __isl_keep isl_aff *aff);
1800 A new local space can be created from a space using
1802 #include <isl/local_space.h>
1803 __isl_give isl_local_space *isl_local_space_from_space(
1804 __isl_take isl_space *space);
1806 They can be inspected, modified, copied and freed using the following functions.
1808 #include <isl/local_space.h>
1809 isl_bool isl_local_space_is_params(
1810 __isl_keep isl_local_space *ls);
1811 isl_bool isl_local_space_is_set(
1812 __isl_keep isl_local_space *ls);
1813 __isl_give isl_space *isl_local_space_get_space(
1814 __isl_keep isl_local_space *ls);
1815 __isl_give isl_aff *isl_local_space_get_div(
1816 __isl_keep isl_local_space *ls, int pos);
1817 __isl_give isl_local_space *isl_local_space_copy(
1818 __isl_keep isl_local_space *ls);
1819 __isl_null isl_local_space *isl_local_space_free(
1820 __isl_take isl_local_space *ls);
1822 Note that C<isl_local_space_get_div> can only be used on local spaces
1825 Two local spaces can be compared using
1827 isl_bool isl_local_space_is_equal(
1828 __isl_keep isl_local_space *ls1,
1829 __isl_keep isl_local_space *ls2);
1831 Local spaces can be created from other local spaces
1832 using the functions described in L</"Unary Operations">
1833 and L</"Binary Operations">.
1835 =head2 Creating New Sets and Relations
1837 C<isl> has functions for creating some standard sets and relations.
1841 =item * Empty sets and relations
1843 __isl_give isl_basic_set *isl_basic_set_empty(
1844 __isl_take isl_space *space);
1845 __isl_give isl_basic_map *isl_basic_map_empty(
1846 __isl_take isl_space *space);
1847 __isl_give isl_set *isl_set_empty(
1848 __isl_take isl_space *space);
1849 __isl_give isl_map *isl_map_empty(
1850 __isl_take isl_space *space);
1851 __isl_give isl_union_set *isl_union_set_empty(
1852 __isl_take isl_space *space);
1853 __isl_give isl_union_map *isl_union_map_empty(
1854 __isl_take isl_space *space);
1856 For C<isl_union_set>s and C<isl_union_map>s, the space
1857 is only used to specify the parameters.
1859 =item * Universe sets and relations
1861 __isl_give isl_basic_set *isl_basic_set_universe(
1862 __isl_take isl_space *space);
1863 __isl_give isl_basic_map *isl_basic_map_universe(
1864 __isl_take isl_space *space);
1865 __isl_give isl_set *isl_set_universe(
1866 __isl_take isl_space *space);
1867 __isl_give isl_map *isl_map_universe(
1868 __isl_take isl_space *space);
1869 __isl_give isl_union_set *isl_union_set_universe(
1870 __isl_take isl_union_set *uset);
1871 __isl_give isl_union_map *isl_union_map_universe(
1872 __isl_take isl_union_map *umap);
1874 The sets and relations constructed by the functions above
1875 contain all integer values, while those constructed by the
1876 functions below only contain non-negative values.
1878 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1879 __isl_take isl_space *space);
1880 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1881 __isl_take isl_space *space);
1882 __isl_give isl_set *isl_set_nat_universe(
1883 __isl_take isl_space *space);
1884 __isl_give isl_map *isl_map_nat_universe(
1885 __isl_take isl_space *space);
1887 =item * Identity relations
1889 __isl_give isl_basic_map *isl_basic_map_identity(
1890 __isl_take isl_space *space);
1891 __isl_give isl_map *isl_map_identity(
1892 __isl_take isl_space *space);
1894 The number of input and output dimensions in C<space> needs
1897 =item * Lexicographic order
1899 __isl_give isl_map *isl_map_lex_lt(
1900 __isl_take isl_space *set_space);
1901 __isl_give isl_map *isl_map_lex_le(
1902 __isl_take isl_space *set_space);
1903 __isl_give isl_map *isl_map_lex_gt(
1904 __isl_take isl_space *set_space);
1905 __isl_give isl_map *isl_map_lex_ge(
1906 __isl_take isl_space *set_space);
1907 __isl_give isl_map *isl_map_lex_lt_first(
1908 __isl_take isl_space *space, unsigned n);
1909 __isl_give isl_map *isl_map_lex_le_first(
1910 __isl_take isl_space *space, unsigned n);
1911 __isl_give isl_map *isl_map_lex_gt_first(
1912 __isl_take isl_space *space, unsigned n);
1913 __isl_give isl_map *isl_map_lex_ge_first(
1914 __isl_take isl_space *space, unsigned n);
1916 The first four functions take a space for a B<set>
1917 and return relations that express that the elements in the domain
1918 are lexicographically less
1919 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1920 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1921 than the elements in the range.
1922 The last four functions take a space for a map
1923 and return relations that express that the first C<n> dimensions
1924 in the domain are lexicographically less
1925 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1926 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1927 than the first C<n> dimensions in the range.
1931 A basic set or relation can be converted to a set or relation
1932 using the following functions.
1934 __isl_give isl_set *isl_set_from_basic_set(
1935 __isl_take isl_basic_set *bset);
1936 __isl_give isl_map *isl_map_from_basic_map(
1937 __isl_take isl_basic_map *bmap);
1939 Sets and relations can be converted to union sets and relations
1940 using the following functions.
1942 __isl_give isl_union_set *isl_union_set_from_basic_set(
1943 __isl_take isl_basic_set *bset);
1944 __isl_give isl_union_map *isl_union_map_from_basic_map(
1945 __isl_take isl_basic_map *bmap);
1946 __isl_give isl_union_set *isl_union_set_from_set(
1947 __isl_take isl_set *set);
1948 __isl_give isl_union_map *isl_union_map_from_map(
1949 __isl_take isl_map *map);
1951 The inverse conversions below can only be used if the input
1952 union set or relation is known to contain elements in exactly one
1955 __isl_give isl_set *isl_set_from_union_set(
1956 __isl_take isl_union_set *uset);
1957 __isl_give isl_map *isl_map_from_union_map(
1958 __isl_take isl_union_map *umap);
1960 Sets and relations can be copied and freed again using the following
1963 __isl_give isl_basic_set *isl_basic_set_copy(
1964 __isl_keep isl_basic_set *bset);
1965 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1966 __isl_give isl_union_set *isl_union_set_copy(
1967 __isl_keep isl_union_set *uset);
1968 __isl_give isl_basic_map *isl_basic_map_copy(
1969 __isl_keep isl_basic_map *bmap);
1970 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1971 __isl_give isl_union_map *isl_union_map_copy(
1972 __isl_keep isl_union_map *umap);
1973 __isl_null isl_basic_set *isl_basic_set_free(
1974 __isl_take isl_basic_set *bset);
1975 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1976 __isl_null isl_union_set *isl_union_set_free(
1977 __isl_take isl_union_set *uset);
1978 __isl_null isl_basic_map *isl_basic_map_free(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1981 __isl_null isl_union_map *isl_union_map_free(
1982 __isl_take isl_union_map *umap);
1984 Other sets and relations can be constructed by starting
1985 from a universe set or relation, adding equality and/or
1986 inequality constraints and then projecting out the
1987 existentially quantified variables, if any.
1988 Constraints can be constructed, manipulated and
1989 added to (or removed from) (basic) sets and relations
1990 using the following functions.
1992 #include <isl/constraint.h>
1993 __isl_give isl_constraint *isl_constraint_alloc_equality(
1994 __isl_take isl_local_space *ls);
1995 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1996 __isl_take isl_local_space *ls);
1997 __isl_give isl_constraint *isl_constraint_set_constant_si(
1998 __isl_take isl_constraint *constraint, int v);
1999 __isl_give isl_constraint *isl_constraint_set_constant_val(
2000 __isl_take isl_constraint *constraint,
2001 __isl_take isl_val *v);
2002 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2003 __isl_take isl_constraint *constraint,
2004 enum isl_dim_type type, int pos, int v);
2005 __isl_give isl_constraint *
2006 isl_constraint_set_coefficient_val(
2007 __isl_take isl_constraint *constraint,
2008 enum isl_dim_type type, int pos,
2009 __isl_take isl_val *v);
2010 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2011 __isl_take isl_basic_map *bmap,
2012 __isl_take isl_constraint *constraint);
2013 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2014 __isl_take isl_basic_set *bset,
2015 __isl_take isl_constraint *constraint);
2016 __isl_give isl_map *isl_map_add_constraint(
2017 __isl_take isl_map *map,
2018 __isl_take isl_constraint *constraint);
2019 __isl_give isl_set *isl_set_add_constraint(
2020 __isl_take isl_set *set,
2021 __isl_take isl_constraint *constraint);
2023 For example, to create a set containing the even integers
2024 between 10 and 42, you would use the following code.
2027 isl_local_space *ls;
2029 isl_basic_set *bset;
2031 space = isl_space_set_alloc(ctx, 0, 2);
2032 bset = isl_basic_set_universe(isl_space_copy(space));
2033 ls = isl_local_space_from_space(space);
2035 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2036 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2037 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2038 bset = isl_basic_set_add_constraint(bset, c);
2040 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2041 c = isl_constraint_set_constant_si(c, -10);
2042 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2043 bset = isl_basic_set_add_constraint(bset, c);
2045 c = isl_constraint_alloc_inequality(ls);
2046 c = isl_constraint_set_constant_si(c, 42);
2047 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2048 bset = isl_basic_set_add_constraint(bset, c);
2050 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2054 isl_basic_set *bset;
2055 bset = isl_basic_set_read_from_str(ctx,
2056 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2058 A basic set or relation can also be constructed from two matrices
2059 describing the equalities and the inequalities.
2061 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2062 __isl_take isl_space *space,
2063 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2064 enum isl_dim_type c1,
2065 enum isl_dim_type c2, enum isl_dim_type c3,
2066 enum isl_dim_type c4);
2067 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2068 __isl_take isl_space *space,
2069 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2070 enum isl_dim_type c1,
2071 enum isl_dim_type c2, enum isl_dim_type c3,
2072 enum isl_dim_type c4, enum isl_dim_type c5);
2074 The C<isl_dim_type> arguments indicate the order in which
2075 different kinds of variables appear in the input matrices
2076 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2077 C<isl_dim_set> and C<isl_dim_div> for sets and
2078 of C<isl_dim_cst>, C<isl_dim_param>,
2079 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2081 A (basic or union) set or relation can also be constructed from a
2082 (union) (piecewise) (multiple) affine expression
2083 or a list of affine expressions
2084 (See L</"Functions">), provided these affine expressions do not
2087 __isl_give isl_basic_map *isl_basic_map_from_aff(
2088 __isl_take isl_aff *aff);
2089 __isl_give isl_map *isl_map_from_aff(
2090 __isl_take isl_aff *aff);
2091 __isl_give isl_set *isl_set_from_pw_aff(
2092 __isl_take isl_pw_aff *pwaff);
2093 __isl_give isl_map *isl_map_from_pw_aff(
2094 __isl_take isl_pw_aff *pwaff);
2095 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2096 __isl_take isl_space *domain_space,
2097 __isl_take isl_aff_list *list);
2098 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2099 __isl_take isl_multi_aff *maff)
2100 __isl_give isl_map *isl_map_from_multi_aff(
2101 __isl_take isl_multi_aff *maff)
2102 __isl_give isl_set *isl_set_from_pw_multi_aff(
2103 __isl_take isl_pw_multi_aff *pma);
2104 __isl_give isl_map *isl_map_from_pw_multi_aff(
2105 __isl_take isl_pw_multi_aff *pma);
2106 __isl_give isl_set *isl_set_from_multi_pw_aff(
2107 __isl_take isl_multi_pw_aff *mpa);
2108 __isl_give isl_map *isl_map_from_multi_pw_aff(
2109 __isl_take isl_multi_pw_aff *mpa);
2110 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2111 __isl_take isl_union_pw_aff *upa);
2112 __isl_give isl_union_map *
2113 isl_union_map_from_union_pw_multi_aff(
2114 __isl_take isl_union_pw_multi_aff *upma);
2115 __isl_give isl_union_map *
2116 isl_union_map_from_multi_union_pw_aff(
2117 __isl_take isl_multi_union_pw_aff *mupa);
2119 The C<domain_space> argument describes the domain of the resulting
2120 basic relation. It is required because the C<list> may consist
2121 of zero affine expressions.
2122 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2123 is not allowed to be zero-dimensional. The domain of the result
2124 is the shared domain of the union piecewise affine elements.
2126 =head2 Inspecting Sets and Relations
2128 Usually, the user should not have to care about the actual constraints
2129 of the sets and maps, but should instead apply the abstract operations
2130 explained in the following sections.
2131 Occasionally, however, it may be required to inspect the individual
2132 coefficients of the constraints. This section explains how to do so.
2133 In these cases, it may also be useful to have C<isl> compute
2134 an explicit representation of the existentially quantified variables.
2136 __isl_give isl_set *isl_set_compute_divs(
2137 __isl_take isl_set *set);
2138 __isl_give isl_map *isl_map_compute_divs(
2139 __isl_take isl_map *map);
2140 __isl_give isl_union_set *isl_union_set_compute_divs(
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_union_map *isl_union_map_compute_divs(
2143 __isl_take isl_union_map *umap);
2145 This explicit representation defines the existentially quantified
2146 variables as integer divisions of the other variables, possibly
2147 including earlier existentially quantified variables.
2148 An explicitly represented existentially quantified variable therefore
2149 has a unique value when the values of the other variables are known.
2151 Alternatively, the existentially quantified variables can be removed
2152 using the following functions, which compute an overapproximation.
2154 #include <isl/set.h>
2155 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2156 __isl_take isl_basic_set *bset);
2157 __isl_give isl_set *isl_set_remove_divs(
2158 __isl_take isl_set *set);
2160 #include <isl/map.h>
2161 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2162 __isl_take isl_basic_map *bmap);
2163 __isl_give isl_map *isl_map_remove_divs(
2164 __isl_take isl_map *map);
2166 #include <isl/union_set.h>
2167 __isl_give isl_union_set *isl_union_set_remove_divs(
2168 __isl_take isl_union_set *bset);
2170 #include <isl/union_map.h>
2171 __isl_give isl_union_map *isl_union_map_remove_divs(
2172 __isl_take isl_union_map *bmap);
2174 It is also possible to only remove those divs that are defined
2175 in terms of a given range of dimensions or only those for which
2176 no explicit representation is known.
2178 __isl_give isl_basic_set *
2179 isl_basic_set_remove_divs_involving_dims(
2180 __isl_take isl_basic_set *bset,
2181 enum isl_dim_type type,
2182 unsigned first, unsigned n);
2183 __isl_give isl_basic_map *
2184 isl_basic_map_remove_divs_involving_dims(
2185 __isl_take isl_basic_map *bmap,
2186 enum isl_dim_type type,
2187 unsigned first, unsigned n);
2188 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2189 __isl_take isl_set *set, enum isl_dim_type type,
2190 unsigned first, unsigned n);
2191 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2192 __isl_take isl_map *map, enum isl_dim_type type,
2193 unsigned first, unsigned n);
2195 __isl_give isl_basic_set *
2196 isl_basic_set_remove_unknown_divs(
2197 __isl_take isl_basic_set *bset);
2198 __isl_give isl_set *isl_set_remove_unknown_divs(
2199 __isl_take isl_set *set);
2200 __isl_give isl_map *isl_map_remove_unknown_divs(
2201 __isl_take isl_map *map);
2203 To iterate over all the sets or maps in a union set or map, use
2205 #include <isl/union_set.h>
2206 isl_stat isl_union_set_foreach_set(
2207 __isl_keep isl_union_set *uset,
2208 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2211 #include <isl/union_map.h>
2212 isl_stat isl_union_map_foreach_map(
2213 __isl_keep isl_union_map *umap,
2214 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2216 isl_bool isl_union_map_every_map(
2217 __isl_keep isl_union_map *umap,
2218 isl_bool (*test)(__isl_keep isl_map *map,
2222 These functions call the callback function once for each
2223 (pair of) space(s) for which there are elements in the input.
2224 The argument to the callback contains all elements in the input
2225 with that (pair of) space(s).
2226 The C<isl_union_map_every_map> variant check whether each
2227 call to the callback returns true and stops checking as soon as one
2228 of these calls returns false.
2230 The number of sets or maps in a union set or map can be obtained
2233 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2234 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2236 To extract the set or map in a given space from a union, use
2238 __isl_give isl_set *isl_union_set_extract_set(
2239 __isl_keep isl_union_set *uset,
2240 __isl_take isl_space *space);
2241 __isl_give isl_map *isl_union_map_extract_map(
2242 __isl_keep isl_union_map *umap,
2243 __isl_take isl_space *space);
2245 To iterate over all the basic sets or maps in a set or map, use
2247 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2248 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2251 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2252 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2256 The callback function C<fn> should return C<isl_stat_ok> if successful and
2257 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2258 occurs, the above functions will return C<isl_stat_error>.
2260 It should be noted that C<isl> does not guarantee that
2261 the basic sets or maps passed to C<fn> are disjoint.
2262 If this is required, then the user should call one of
2263 the following functions first.
2265 __isl_give isl_set *isl_set_make_disjoint(
2266 __isl_take isl_set *set);
2267 __isl_give isl_map *isl_map_make_disjoint(
2268 __isl_take isl_map *map);
2270 The number of basic sets in a set can be obtained
2271 or the number of basic maps in a map can be obtained
2274 #include <isl/set.h>
2275 int isl_set_n_basic_set(__isl_keep isl_set *set);
2277 #include <isl/map.h>
2278 int isl_map_n_basic_map(__isl_keep isl_map *map);
2280 It is also possible to obtain a list of basic sets from a set
2281 or union set and a list of basic maps from a map.
2283 #include <isl/set.h>
2284 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2285 __isl_keep isl_set *set);
2287 #include <isl/union_set.h>
2288 __isl_give isl_basic_set_list *
2289 isl_union_set_get_basic_set_list(
2290 __isl_keep isl_union_set *uset);
2292 #include <isl/map.h>
2293 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2294 __isl_keep isl_map *map);
2296 The returned list can be manipulated using the functions in L<"Lists">.
2298 To iterate over the constraints of a basic set or map, use
2300 #include <isl/constraint.h>
2302 int isl_basic_set_n_constraint(
2303 __isl_keep isl_basic_set *bset);
2304 isl_stat isl_basic_set_foreach_constraint(
2305 __isl_keep isl_basic_set *bset,
2306 isl_stat (*fn)(__isl_take isl_constraint *c,
2309 int isl_basic_map_n_constraint(
2310 __isl_keep isl_basic_map *bmap);
2311 isl_stat isl_basic_map_foreach_constraint(
2312 __isl_keep isl_basic_map *bmap,
2313 isl_stat (*fn)(__isl_take isl_constraint *c,
2316 __isl_null isl_constraint *isl_constraint_free(
2317 __isl_take isl_constraint *c);
2319 Again, the callback function C<fn> should return C<isl_stat_ok>
2321 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2322 occurs, the above functions will return C<isl_stat_error>.
2323 The constraint C<c> represents either an equality or an inequality.
2324 Use the following function to find out whether a constraint
2325 represents an equality. If not, it represents an inequality.
2327 isl_bool isl_constraint_is_equality(
2328 __isl_keep isl_constraint *constraint);
2330 It is also possible to obtain a list of constraints from a basic
2333 #include <isl/constraint.h>
2334 __isl_give isl_constraint_list *
2335 isl_basic_map_get_constraint_list(
2336 __isl_keep isl_basic_map *bmap);
2337 __isl_give isl_constraint_list *
2338 isl_basic_set_get_constraint_list(
2339 __isl_keep isl_basic_set *bset);
2341 These functions require that all existentially quantified variables
2342 have an explicit representation.
2343 The returned list can be manipulated using the functions in L<"Lists">.
2345 The coefficients of the constraints can be inspected using
2346 the following functions.
2348 isl_bool isl_constraint_is_lower_bound(
2349 __isl_keep isl_constraint *constraint,
2350 enum isl_dim_type type, unsigned pos);
2351 isl_bool isl_constraint_is_upper_bound(
2352 __isl_keep isl_constraint *constraint,
2353 enum isl_dim_type type, unsigned pos);
2354 __isl_give isl_val *isl_constraint_get_constant_val(
2355 __isl_keep isl_constraint *constraint);
2356 __isl_give isl_val *isl_constraint_get_coefficient_val(
2357 __isl_keep isl_constraint *constraint,
2358 enum isl_dim_type type, int pos);
2360 The explicit representations of the existentially quantified
2361 variables can be inspected using the following function.
2362 Note that the user is only allowed to use this function
2363 if the inspected set or map is the result of a call
2364 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2365 The existentially quantified variable is equal to the floor
2366 of the returned affine expression. The affine expression
2367 itself can be inspected using the functions in
2370 __isl_give isl_aff *isl_constraint_get_div(
2371 __isl_keep isl_constraint *constraint, int pos);
2373 To obtain the constraints of a basic set or map in matrix
2374 form, use the following functions.
2376 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2377 __isl_keep isl_basic_set *bset,
2378 enum isl_dim_type c1, enum isl_dim_type c2,
2379 enum isl_dim_type c3, enum isl_dim_type c4);
2380 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2381 __isl_keep isl_basic_set *bset,
2382 enum isl_dim_type c1, enum isl_dim_type c2,
2383 enum isl_dim_type c3, enum isl_dim_type c4);
2384 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2385 __isl_keep isl_basic_map *bmap,
2386 enum isl_dim_type c1,
2387 enum isl_dim_type c2, enum isl_dim_type c3,
2388 enum isl_dim_type c4, enum isl_dim_type c5);
2389 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2390 __isl_keep isl_basic_map *bmap,
2391 enum isl_dim_type c1,
2392 enum isl_dim_type c2, enum isl_dim_type c3,
2393 enum isl_dim_type c4, enum isl_dim_type c5);
2395 The C<isl_dim_type> arguments dictate the order in which
2396 different kinds of variables appear in the resulting matrix.
2397 For set inputs, they should be a permutation of
2398 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2399 For map inputs, they should be a permutation of
2400 C<isl_dim_cst>, C<isl_dim_param>,
2401 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2405 Points are elements of a set. They can be used to construct
2406 simple sets (boxes) or they can be used to represent the
2407 individual elements of a set.
2408 The zero point (the origin) can be created using
2410 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2412 The coordinates of a point can be inspected, set and changed
2415 __isl_give isl_val *isl_point_get_coordinate_val(
2416 __isl_keep isl_point *pnt,
2417 enum isl_dim_type type, int pos);
2418 __isl_give isl_point *isl_point_set_coordinate_val(
2419 __isl_take isl_point *pnt,
2420 enum isl_dim_type type, int pos,
2421 __isl_take isl_val *v);
2423 __isl_give isl_point *isl_point_add_ui(
2424 __isl_take isl_point *pnt,
2425 enum isl_dim_type type, int pos, unsigned val);
2426 __isl_give isl_point *isl_point_sub_ui(
2427 __isl_take isl_point *pnt,
2428 enum isl_dim_type type, int pos, unsigned val);
2430 Points can be copied or freed using
2432 __isl_give isl_point *isl_point_copy(
2433 __isl_keep isl_point *pnt);
2434 __isl_null isl_point *isl_point_free(
2435 __isl_take isl_point *pnt);
2437 A singleton set can be created from a point using
2439 __isl_give isl_basic_set *isl_basic_set_from_point(
2440 __isl_take isl_point *pnt);
2441 __isl_give isl_set *isl_set_from_point(
2442 __isl_take isl_point *pnt);
2443 __isl_give isl_union_set *isl_union_set_from_point(
2444 __isl_take isl_point *pnt);
2446 and a box can be created from two opposite extremal points using
2448 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2449 __isl_take isl_point *pnt1,
2450 __isl_take isl_point *pnt2);
2451 __isl_give isl_set *isl_set_box_from_points(
2452 __isl_take isl_point *pnt1,
2453 __isl_take isl_point *pnt2);
2455 All elements of a B<bounded> (union) set can be enumerated using
2456 the following functions.
2458 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2459 isl_stat (*fn)(__isl_take isl_point *pnt,
2462 isl_stat isl_union_set_foreach_point(
2463 __isl_keep isl_union_set *uset,
2464 isl_stat (*fn)(__isl_take isl_point *pnt,
2468 The function C<fn> is called for each integer point in
2469 C<set> with as second argument the last argument of
2470 the C<isl_set_foreach_point> call. The function C<fn>
2471 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2472 In the latter case, C<isl_set_foreach_point> will stop
2473 enumerating and return C<isl_stat_error> as well.
2474 If the enumeration is performed successfully and to completion,
2475 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2477 To obtain a single point of a (basic or union) set, use
2479 __isl_give isl_point *isl_basic_set_sample_point(
2480 __isl_take isl_basic_set *bset);
2481 __isl_give isl_point *isl_set_sample_point(
2482 __isl_take isl_set *set);
2483 __isl_give isl_point *isl_union_set_sample_point(
2484 __isl_take isl_union_set *uset);
2486 If C<set> does not contain any (integer) points, then the
2487 resulting point will be ``void'', a property that can be
2490 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2494 Besides sets and relation, C<isl> also supports various types of functions.
2495 Each of these types is derived from the value type (see L</"Values">)
2496 or from one of two primitive function types
2497 through the application of zero or more type constructors.
2498 We first describe the primitive type and then we describe
2499 the types derived from these primitive types.
2501 =head3 Primitive Functions
2503 C<isl> support two primitive function types, quasi-affine
2504 expressions and quasipolynomials.
2505 A quasi-affine expression is defined either over a parameter
2506 space or over a set and is composed of integer constants,
2507 parameters and set variables, addition, subtraction and
2508 integer division by an integer constant.
2509 For example, the quasi-affine expression
2511 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2513 maps C<x> to C<2*floor((4 n + x)/9>.
2514 A quasipolynomial is a polynomial expression in quasi-affine
2515 expression. That is, it additionally allows for multiplication.
2516 Note, though, that it is not allowed to construct an integer
2517 division of an expression involving multiplications.
2518 Here is an example of a quasipolynomial that is not
2519 quasi-affine expression
2521 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2523 Note that the external representations of quasi-affine expressions
2524 and quasipolynomials are different. Quasi-affine expressions
2525 use a notation with square brackets just like binary relations,
2526 while quasipolynomials do not. This might change at some point.
2528 If a primitive function is defined over a parameter space,
2529 then the space of the function itself is that of a set.
2530 If it is defined over a set, then the space of the function
2531 is that of a relation. In both cases, the set space (or
2532 the output space) is single-dimensional, anonymous and unstructured.
2533 To create functions with multiple dimensions or with other kinds
2534 of set or output spaces, use multiple expressions
2535 (see L</"Multiple Expressions">).
2539 =item * Quasi-affine Expressions
2541 Besides the expressions described above, a quasi-affine
2542 expression can also be set to NaN. Such expressions
2543 typically represent a failure to represent a result
2544 as a quasi-affine expression.
2546 The zero quasi affine expression or the quasi affine expression
2547 that is equal to a given value, parameter or
2548 a specified dimension on a given domain can be created using
2550 #include <isl/aff.h>
2551 __isl_give isl_aff *isl_aff_zero_on_domain(
2552 __isl_take isl_local_space *ls);
2553 __isl_give isl_aff *isl_aff_val_on_domain(
2554 __isl_take isl_local_space *ls,
2555 __isl_take isl_val *val);
2556 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2557 __isl_take isl_space *space,
2558 __isl_take isl_id *id);
2559 __isl_give isl_aff *isl_aff_var_on_domain(
2560 __isl_take isl_local_space *ls,
2561 enum isl_dim_type type, unsigned pos);
2562 __isl_give isl_aff *isl_aff_nan_on_domain(
2563 __isl_take isl_local_space *ls);
2565 The space passed to C<isl_aff_param_on_domain_space_id>
2566 is required to have a parameter with the given identifier.
2568 Quasi affine expressions can be copied and freed using
2570 #include <isl/aff.h>
2571 __isl_give isl_aff *isl_aff_copy(
2572 __isl_keep isl_aff *aff);
2573 __isl_null isl_aff *isl_aff_free(
2574 __isl_take isl_aff *aff);
2576 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2577 using the following function. The constraint is required to have
2578 a non-zero coefficient for the specified dimension.
2580 #include <isl/constraint.h>
2581 __isl_give isl_aff *isl_constraint_get_bound(
2582 __isl_keep isl_constraint *constraint,
2583 enum isl_dim_type type, int pos);
2585 The entire affine expression of the constraint can also be extracted
2586 using the following function.
2588 #include <isl/constraint.h>
2589 __isl_give isl_aff *isl_constraint_get_aff(
2590 __isl_keep isl_constraint *constraint);
2592 Conversely, an equality constraint equating
2593 the affine expression to zero or an inequality constraint enforcing
2594 the affine expression to be non-negative, can be constructed using
2596 __isl_give isl_constraint *isl_equality_from_aff(
2597 __isl_take isl_aff *aff);
2598 __isl_give isl_constraint *isl_inequality_from_aff(
2599 __isl_take isl_aff *aff);
2601 The coefficients and the integer divisions of an affine expression
2602 can be inspected using the following functions.
2604 #include <isl/aff.h>
2605 __isl_give isl_val *isl_aff_get_constant_val(
2606 __isl_keep isl_aff *aff);
2607 __isl_give isl_val *isl_aff_get_coefficient_val(
2608 __isl_keep isl_aff *aff,
2609 enum isl_dim_type type, int pos);
2610 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2611 enum isl_dim_type type, int pos);
2612 __isl_give isl_val *isl_aff_get_denominator_val(
2613 __isl_keep isl_aff *aff);
2614 __isl_give isl_aff *isl_aff_get_div(
2615 __isl_keep isl_aff *aff, int pos);
2617 They can be modified using the following functions.
2619 #include <isl/aff.h>
2620 __isl_give isl_aff *isl_aff_set_constant_si(
2621 __isl_take isl_aff *aff, int v);
2622 __isl_give isl_aff *isl_aff_set_constant_val(
2623 __isl_take isl_aff *aff, __isl_take isl_val *v);
2624 __isl_give isl_aff *isl_aff_set_coefficient_si(
2625 __isl_take isl_aff *aff,
2626 enum isl_dim_type type, int pos, int v);
2627 __isl_give isl_aff *isl_aff_set_coefficient_val(
2628 __isl_take isl_aff *aff,
2629 enum isl_dim_type type, int pos,
2630 __isl_take isl_val *v);
2632 __isl_give isl_aff *isl_aff_add_constant_si(
2633 __isl_take isl_aff *aff, int v);
2634 __isl_give isl_aff *isl_aff_add_constant_val(
2635 __isl_take isl_aff *aff, __isl_take isl_val *v);
2636 __isl_give isl_aff *isl_aff_add_constant_num_si(
2637 __isl_take isl_aff *aff, int v);
2638 __isl_give isl_aff *isl_aff_add_coefficient_si(
2639 __isl_take isl_aff *aff,
2640 enum isl_dim_type type, int pos, int v);
2641 __isl_give isl_aff *isl_aff_add_coefficient_val(
2642 __isl_take isl_aff *aff,
2643 enum isl_dim_type type, int pos,
2644 __isl_take isl_val *v);
2646 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2647 set the I<numerator> of the constant or coefficient, while
2648 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2649 the constant or coefficient as a whole.
2650 The C<add_constant> and C<add_coefficient> functions add an integer
2651 or rational value to
2652 the possibly rational constant or coefficient.
2653 The C<add_constant_num> functions add an integer value to
2656 =item * Quasipolynomials
2658 Some simple quasipolynomials can be created using the following functions.
2660 #include <isl/polynomial.h>
2661 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2662 __isl_take isl_space *domain);
2663 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2664 __isl_take isl_space *domain);
2665 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2666 __isl_take isl_space *domain);
2667 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2668 __isl_take isl_space *domain);
2669 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2670 __isl_take isl_space *domain);
2671 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2672 __isl_take isl_space *domain,
2673 __isl_take isl_val *val);
2674 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2675 __isl_take isl_space *domain,
2676 enum isl_dim_type type, unsigned pos);
2677 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2678 __isl_take isl_aff *aff);
2680 Recall that the space in which a quasipolynomial lives is a map space
2681 with a one-dimensional range. The C<domain> argument in some of
2682 the functions above corresponds to the domain of this map space.
2684 Quasipolynomials can be copied and freed again using the following
2687 #include <isl/polynomial.h>
2688 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2689 __isl_keep isl_qpolynomial *qp);
2690 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2691 __isl_take isl_qpolynomial *qp);
2693 The constant term of a quasipolynomial can be extracted using
2695 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2696 __isl_keep isl_qpolynomial *qp);
2698 To iterate over all terms in a quasipolynomial,
2701 isl_stat isl_qpolynomial_foreach_term(
2702 __isl_keep isl_qpolynomial *qp,
2703 isl_stat (*fn)(__isl_take isl_term *term,
2704 void *user), void *user);
2706 The terms themselves can be inspected and freed using
2709 unsigned isl_term_dim(__isl_keep isl_term *term,
2710 enum isl_dim_type type);
2711 __isl_give isl_val *isl_term_get_coefficient_val(
2712 __isl_keep isl_term *term);
2713 int isl_term_get_exp(__isl_keep isl_term *term,
2714 enum isl_dim_type type, unsigned pos);
2715 __isl_give isl_aff *isl_term_get_div(
2716 __isl_keep isl_term *term, unsigned pos);
2717 void isl_term_free(__isl_take isl_term *term);
2719 Each term is a product of parameters, set variables and
2720 integer divisions. The function C<isl_term_get_exp>
2721 returns the exponent of a given dimensions in the given term.
2727 A reduction represents a maximum or a minimum of its
2729 The only reduction type defined by C<isl> is
2730 C<isl_qpolynomial_fold>.
2732 There are currently no functions to directly create such
2733 objects, but they do appear in the piecewise quasipolynomial
2734 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2736 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2738 Reductions can be copied and freed using
2739 the following functions.
2741 #include <isl/polynomial.h>
2742 __isl_give isl_qpolynomial_fold *
2743 isl_qpolynomial_fold_copy(
2744 __isl_keep isl_qpolynomial_fold *fold);
2745 void isl_qpolynomial_fold_free(
2746 __isl_take isl_qpolynomial_fold *fold);
2748 To iterate over all quasipolynomials in a reduction, use
2750 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2751 __isl_keep isl_qpolynomial_fold *fold,
2752 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2753 void *user), void *user);
2755 =head3 Multiple Expressions
2757 A multiple expression represents a sequence of zero or
2758 more base expressions, all defined on the same domain space.
2759 The domain space of the multiple expression is the same
2760 as that of the base expressions, but the range space
2761 can be any space. In case the base expressions have
2762 a set space, the corresponding multiple expression
2763 also has a set space.
2764 Objects of the value type do not have an associated space.
2765 The space of a multiple value is therefore always a set space.
2766 Similarly, the space of a multiple union piecewise
2767 affine expression is always a set space.
2768 If the base expressions are not total, then
2769 a corresponding zero-dimensional multiple expression may
2770 have an explicit domain that keeps track of the domain
2771 outside of any base expressions.
2773 The multiple expression types defined by C<isl>
2774 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2775 C<isl_multi_union_pw_aff>.
2777 A multiple expression with the value zero for
2778 each output (or set) dimension can be created
2779 using the following functions.
2781 #include <isl/val.h>
2782 __isl_give isl_multi_val *isl_multi_val_zero(
2783 __isl_take isl_space *space);
2785 #include <isl/aff.h>
2786 __isl_give isl_multi_aff *isl_multi_aff_zero(
2787 __isl_take isl_space *space);
2788 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2789 __isl_take isl_space *space);
2790 __isl_give isl_multi_union_pw_aff *
2791 isl_multi_union_pw_aff_zero(
2792 __isl_take isl_space *space);
2794 Since there is no canonical way of representing a zero
2795 value of type C<isl_union_pw_aff>, the space passed
2796 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2798 An identity function can be created using the following
2799 functions. The space needs to be that of a relation
2800 with the same number of input and output dimensions.
2802 #include <isl/aff.h>
2803 __isl_give isl_multi_aff *isl_multi_aff_identity(
2804 __isl_take isl_space *space);
2805 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2806 __isl_take isl_space *space);
2808 A function that performs a projection on a universe
2809 relation or set can be created using the following functions.
2810 See also the corresponding
2811 projection operations in L</"Unary Operations">.
2813 #include <isl/aff.h>
2814 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2815 __isl_take isl_space *space);
2816 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2817 __isl_take isl_space *space);
2818 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2819 __isl_take isl_space *space,
2820 enum isl_dim_type type,
2821 unsigned first, unsigned n);
2823 A multiple expression can be created from a single
2824 base expression using the following functions.
2825 The space of the created multiple expression is the same
2826 as that of the base expression, except for
2827 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2828 lives in a parameter space and the output lives
2829 in a single-dimensional set space.
2831 #include <isl/aff.h>
2832 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2833 __isl_take isl_aff *aff);
2834 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2835 __isl_take isl_pw_aff *pa);
2836 __isl_give isl_multi_union_pw_aff *
2837 isl_multi_union_pw_aff_from_union_pw_aff(
2838 __isl_take isl_union_pw_aff *upa);
2840 A multiple expression can be created from a list
2841 of base expression in a specified space.
2842 The domain of this space needs to be the same
2843 as the domains of the base expressions in the list.
2844 If the base expressions have a set space (or no associated space),
2845 then this space also needs to be a set space.
2847 #include <isl/val.h>
2848 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2849 __isl_take isl_space *space,
2850 __isl_take isl_val_list *list);
2852 #include <isl/aff.h>
2853 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2854 __isl_take isl_space *space,
2855 __isl_take isl_aff_list *list);
2856 __isl_give isl_multi_pw_aff *
2857 isl_multi_pw_aff_from_pw_aff_list(
2858 __isl_take isl_space *space,
2859 __isl_take isl_pw_aff_list *list);
2860 __isl_give isl_multi_union_pw_aff *
2861 isl_multi_union_pw_aff_from_union_pw_aff_list(
2862 __isl_take isl_space *space,
2863 __isl_take isl_union_pw_aff_list *list);
2865 As a convenience, a multiple piecewise expression can
2866 also be created from a multiple expression.
2867 Each piecewise expression in the result has a single
2870 #include <isl/aff.h>
2871 __isl_give isl_multi_pw_aff *
2872 isl_multi_pw_aff_from_multi_aff(
2873 __isl_take isl_multi_aff *ma);
2875 Similarly, a multiple union expression can be
2876 created from a multiple expression.
2878 #include <isl/aff.h>
2879 __isl_give isl_multi_union_pw_aff *
2880 isl_multi_union_pw_aff_from_multi_aff(
2881 __isl_take isl_multi_aff *ma);
2882 __isl_give isl_multi_union_pw_aff *
2883 isl_multi_union_pw_aff_from_multi_pw_aff(
2884 __isl_take isl_multi_pw_aff *mpa);
2886 A multiple quasi-affine expression can be created from
2887 a multiple value with a given domain space using the following
2890 #include <isl/aff.h>
2891 __isl_give isl_multi_aff *
2892 isl_multi_aff_multi_val_on_space(
2893 __isl_take isl_space *space,
2894 __isl_take isl_multi_val *mv);
2897 a multiple union piecewise affine expression can be created from
2898 a multiple value with a given domain or
2899 a (piecewise) multiple affine expression with a given domain
2900 using the following functions.
2902 #include <isl/aff.h>
2903 __isl_give isl_multi_union_pw_aff *
2904 isl_multi_union_pw_aff_multi_val_on_domain(
2905 __isl_take isl_union_set *domain,
2906 __isl_take isl_multi_val *mv);
2907 __isl_give isl_multi_union_pw_aff *
2908 isl_multi_union_pw_aff_multi_aff_on_domain(
2909 __isl_take isl_union_set *domain,
2910 __isl_take isl_multi_aff *ma);
2911 __isl_give isl_multi_union_pw_aff *
2912 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2913 __isl_take isl_union_set *domain,
2914 __isl_take isl_pw_multi_aff *pma);
2916 Multiple expressions can be copied and freed using
2917 the following functions.
2919 #include <isl/val.h>
2920 __isl_give isl_multi_val *isl_multi_val_copy(
2921 __isl_keep isl_multi_val *mv);
2922 __isl_null isl_multi_val *isl_multi_val_free(
2923 __isl_take isl_multi_val *mv);
2925 #include <isl/aff.h>
2926 __isl_give isl_multi_aff *isl_multi_aff_copy(
2927 __isl_keep isl_multi_aff *maff);
2928 __isl_null isl_multi_aff *isl_multi_aff_free(
2929 __isl_take isl_multi_aff *maff);
2930 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2931 __isl_keep isl_multi_pw_aff *mpa);
2932 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2933 __isl_take isl_multi_pw_aff *mpa);
2934 __isl_give isl_multi_union_pw_aff *
2935 isl_multi_union_pw_aff_copy(
2936 __isl_keep isl_multi_union_pw_aff *mupa);
2937 __isl_null isl_multi_union_pw_aff *
2938 isl_multi_union_pw_aff_free(
2939 __isl_take isl_multi_union_pw_aff *mupa);
2941 The base expression at a given position of a multiple
2942 expression can be extracted using the following functions.
2944 #include <isl/val.h>
2945 __isl_give isl_val *isl_multi_val_get_val(
2946 __isl_keep isl_multi_val *mv, int pos);
2948 #include <isl/aff.h>
2949 __isl_give isl_aff *isl_multi_aff_get_aff(
2950 __isl_keep isl_multi_aff *multi, int pos);
2951 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2952 __isl_keep isl_multi_pw_aff *mpa, int pos);
2953 __isl_give isl_union_pw_aff *
2954 isl_multi_union_pw_aff_get_union_pw_aff(
2955 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2957 It can be replaced using the following functions.
2959 #include <isl/val.h>
2960 __isl_give isl_multi_val *isl_multi_val_set_val(
2961 __isl_take isl_multi_val *mv, int pos,
2962 __isl_take isl_val *val);
2964 #include <isl/aff.h>
2965 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2966 __isl_take isl_multi_aff *multi, int pos,
2967 __isl_take isl_aff *aff);
2968 __isl_give isl_multi_union_pw_aff *
2969 isl_multi_union_pw_aff_set_union_pw_aff(
2970 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2971 __isl_take isl_union_pw_aff *upa);
2973 As a convenience, a sequence of base expressions that have
2974 their domains in a given space can be extracted from a sequence
2975 of union expressions using the following function.
2977 #include <isl/aff.h>
2978 __isl_give isl_multi_pw_aff *
2979 isl_multi_union_pw_aff_extract_multi_pw_aff(
2980 __isl_keep isl_multi_union_pw_aff *mupa,
2981 __isl_take isl_space *space);
2983 Note that there is a difference between C<isl_multi_union_pw_aff>
2984 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2985 of unions of piecewise expressions, while the second is a union
2986 of piecewise sequences. In particular, multiple affine expressions
2987 in an C<isl_union_pw_multi_aff> may live in different spaces,
2988 while there is only a single multiple expression in
2989 an C<isl_multi_union_pw_aff>, which can therefore only live
2990 in a single space. This means that not every
2991 C<isl_union_pw_multi_aff> can be converted to
2992 an C<isl_multi_union_pw_aff>. Conversely, the elements
2993 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2994 while each multiple expression inside an C<isl_union_pw_multi_aff>
2995 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2996 of dimension greater than one may therefore not be exact.
2997 The following functions can
2998 be used to perform these conversions when they are possible.
3000 #include <isl/aff.h>
3001 __isl_give isl_multi_union_pw_aff *
3002 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3003 __isl_take isl_union_pw_multi_aff *upma);
3004 __isl_give isl_union_pw_multi_aff *
3005 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3006 __isl_take isl_multi_union_pw_aff *mupa);
3008 =head3 Piecewise Expressions
3010 A piecewise expression is an expression that is described
3011 using zero or more base expression defined over the same
3012 number of cells in the domain space of the base expressions.
3013 All base expressions are defined over the same
3014 domain space and the cells are disjoint.
3015 The space of a piecewise expression is the same as
3016 that of the base expressions.
3017 If the union of the cells is a strict subset of the domain
3018 space, then the value of the piecewise expression outside
3019 this union is different for types derived from quasi-affine
3020 expressions and those derived from quasipolynomials.
3021 Piecewise expressions derived from quasi-affine expressions
3022 are considered to be undefined outside the union of their cells.
3023 Piecewise expressions derived from quasipolynomials
3024 are considered to be zero outside the union of their cells.
3026 Piecewise quasipolynomials are mainly used by the C<barvinok>
3027 library for representing the number of elements in a parametric set or map.
3028 For example, the piecewise quasipolynomial
3030 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3032 represents the number of points in the map
3034 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3036 The piecewise expression types defined by C<isl>
3037 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3038 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3040 A piecewise expression with no cells can be created using
3041 the following functions.
3043 #include <isl/aff.h>
3044 __isl_give isl_pw_aff *isl_pw_aff_empty(
3045 __isl_take isl_space *space);
3046 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3047 __isl_take isl_space *space);
3049 A piecewise expression with a single universe cell can be
3050 created using the following functions.
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3054 __isl_take isl_aff *aff);
3055 __isl_give isl_pw_multi_aff *
3056 isl_pw_multi_aff_from_multi_aff(
3057 __isl_take isl_multi_aff *ma);
3059 #include <isl/polynomial.h>
3060 __isl_give isl_pw_qpolynomial *
3061 isl_pw_qpolynomial_from_qpolynomial(
3062 __isl_take isl_qpolynomial *qp);
3064 A piecewise expression with a single specified cell can be
3065 created using the following functions.
3067 #include <isl/aff.h>
3068 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3069 __isl_take isl_set *set, __isl_take isl_aff *aff);
3070 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3071 __isl_take isl_set *set,
3072 __isl_take isl_multi_aff *maff);
3074 #include <isl/polynomial.h>
3075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3076 __isl_take isl_set *set,
3077 __isl_take isl_qpolynomial *qp);
3079 The following convenience functions first create a base expression and
3080 then create a piecewise expression over a universe domain.
3082 #include <isl/aff.h>
3083 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3084 __isl_take isl_local_space *ls);
3085 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3086 __isl_take isl_local_space *ls,
3087 enum isl_dim_type type, unsigned pos);
3088 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3089 __isl_take isl_local_space *ls);
3090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3091 __isl_take isl_space *space);
3092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3093 __isl_take isl_space *space);
3094 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3095 __isl_take isl_space *space);
3096 __isl_give isl_pw_multi_aff *
3097 isl_pw_multi_aff_project_out_map(
3098 __isl_take isl_space *space,
3099 enum isl_dim_type type,
3100 unsigned first, unsigned n);
3102 #include <isl/polynomial.h>
3103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3104 __isl_take isl_space *space);
3106 The following convenience functions first create a base expression and
3107 then create a piecewise expression over a given domain.
3109 #include <isl/aff.h>
3110 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3111 __isl_take isl_set *domain,
3112 __isl_take isl_val *v);
3113 __isl_give isl_pw_multi_aff *
3114 isl_pw_multi_aff_multi_val_on_domain(
3115 __isl_take isl_set *domain,
3116 __isl_take isl_multi_val *mv);
3118 As a convenience, a piecewise multiple expression can
3119 also be created from a piecewise expression.
3120 Each multiple expression in the result is derived
3121 from the corresponding base expression.
3123 #include <isl/aff.h>
3124 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3125 __isl_take isl_pw_aff *pa);
3127 Similarly, a piecewise quasipolynomial can be
3128 created from a piecewise quasi-affine expression using
3129 the following function.
3131 #include <isl/polynomial.h>
3132 __isl_give isl_pw_qpolynomial *
3133 isl_pw_qpolynomial_from_pw_aff(
3134 __isl_take isl_pw_aff *pwaff);
3136 Piecewise expressions can be copied and freed using the following functions.
3138 #include <isl/aff.h>
3139 __isl_give isl_pw_aff *isl_pw_aff_copy(
3140 __isl_keep isl_pw_aff *pwaff);
3141 __isl_null isl_pw_aff *isl_pw_aff_free(
3142 __isl_take isl_pw_aff *pwaff);
3143 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3144 __isl_keep isl_pw_multi_aff *pma);
3145 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3146 __isl_take isl_pw_multi_aff *pma);
3148 #include <isl/polynomial.h>
3149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3150 __isl_keep isl_pw_qpolynomial *pwqp);
3151 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3152 __isl_take isl_pw_qpolynomial *pwqp);
3153 __isl_give isl_pw_qpolynomial_fold *
3154 isl_pw_qpolynomial_fold_copy(
3155 __isl_keep isl_pw_qpolynomial_fold *pwf);
3156 __isl_null isl_pw_qpolynomial_fold *
3157 isl_pw_qpolynomial_fold_free(
3158 __isl_take isl_pw_qpolynomial_fold *pwf);
3160 To iterate over the different cells of a piecewise expression,
3161 use the following functions.
3163 #include <isl/aff.h>
3164 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3165 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3166 isl_stat isl_pw_aff_foreach_piece(
3167 __isl_keep isl_pw_aff *pwaff,
3168 isl_stat (*fn)(__isl_take isl_set *set,
3169 __isl_take isl_aff *aff,
3170 void *user), void *user);
3171 int isl_pw_multi_aff_n_piece(
3172 __isl_keep isl_pw_multi_aff *pma);
3173 isl_stat isl_pw_multi_aff_foreach_piece(
3174 __isl_keep isl_pw_multi_aff *pma,
3175 isl_stat (*fn)(__isl_take isl_set *set,
3176 __isl_take isl_multi_aff *maff,
3177 void *user), void *user);
3179 #include <isl/polynomial.h>
3180 int isl_pw_qpolynomial_n_piece(
3181 __isl_keep isl_pw_qpolynomial *pwqp);
3182 isl_stat isl_pw_qpolynomial_foreach_piece(
3183 __isl_keep isl_pw_qpolynomial *pwqp,
3184 isl_stat (*fn)(__isl_take isl_set *set,
3185 __isl_take isl_qpolynomial *qp,
3186 void *user), void *user);
3187 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3188 __isl_keep isl_pw_qpolynomial *pwqp,
3189 isl_stat (*fn)(__isl_take isl_set *set,
3190 __isl_take isl_qpolynomial *qp,
3191 void *user), void *user);
3192 int isl_pw_qpolynomial_fold_n_piece(
3193 __isl_keep isl_pw_qpolynomial_fold *pwf);
3194 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3195 __isl_keep isl_pw_qpolynomial_fold *pwf,
3196 isl_stat (*fn)(__isl_take isl_set *set,
3197 __isl_take isl_qpolynomial_fold *fold,
3198 void *user), void *user);
3199 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3200 __isl_keep isl_pw_qpolynomial_fold *pwf,
3201 isl_stat (*fn)(__isl_take isl_set *set,
3202 __isl_take isl_qpolynomial_fold *fold,
3203 void *user), void *user);
3205 As usual, the function C<fn> should return C<isl_stat_ok> on success
3206 and C<isl_stat_error> on failure. The difference between
3207 C<isl_pw_qpolynomial_foreach_piece> and
3208 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3209 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3210 compute unique representations for all existentially quantified
3211 variables and then turn these existentially quantified variables
3212 into extra set variables, adapting the associated quasipolynomial
3213 accordingly. This means that the C<set> passed to C<fn>
3214 will not have any existentially quantified variables, but that
3215 the dimensions of the sets may be different for different
3216 invocations of C<fn>.
3217 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3218 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3220 A piecewise expression consisting of the expressions at a given
3221 position of a piecewise multiple expression can be extracted
3222 using the following function.
3224 #include <isl/aff.h>
3225 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3226 __isl_keep isl_pw_multi_aff *pma, int pos);
3228 These expressions can be replaced using the following function.
3230 #include <isl/aff.h>
3231 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3232 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3233 __isl_take isl_pw_aff *pa);
3235 Note that there is a difference between C<isl_multi_pw_aff> and
3236 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3237 affine expressions, while the second is a piecewise sequence
3238 of affine expressions. In particular, each of the piecewise
3239 affine expressions in an C<isl_multi_pw_aff> may have a different
3240 domain, while all multiple expressions associated to a cell
3241 in an C<isl_pw_multi_aff> have the same domain.
3242 It is possible to convert between the two, but when converting
3243 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3244 of the result is the intersection of the domains of the input.
3245 The reverse conversion is exact.
3247 #include <isl/aff.h>
3248 __isl_give isl_pw_multi_aff *
3249 isl_pw_multi_aff_from_multi_pw_aff(
3250 __isl_take isl_multi_pw_aff *mpa);
3251 __isl_give isl_multi_pw_aff *
3252 isl_multi_pw_aff_from_pw_multi_aff(
3253 __isl_take isl_pw_multi_aff *pma);
3255 =head3 Union Expressions
3257 A union expression collects base expressions defined
3258 over different domains. The space of a union expression
3259 is that of the shared parameter space.
3261 The union expression types defined by C<isl>
3262 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3263 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3265 C<isl_union_pw_aff>,
3266 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3267 there can be at most one base expression for a given domain space.
3269 C<isl_union_pw_multi_aff>,
3270 there can be multiple such expressions for a given domain space,
3271 but the domains of these expressions need to be disjoint.
3273 An empty union expression can be created using the following functions.
3275 #include <isl/aff.h>
3276 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3277 __isl_take isl_space *space);
3278 __isl_give isl_union_pw_multi_aff *
3279 isl_union_pw_multi_aff_empty(
3280 __isl_take isl_space *space);
3282 #include <isl/polynomial.h>
3283 __isl_give isl_union_pw_qpolynomial *
3284 isl_union_pw_qpolynomial_zero(
3285 __isl_take isl_space *space);
3287 A union expression containing a single base expression
3288 can be created using the following functions.
3290 #include <isl/aff.h>
3291 __isl_give isl_union_pw_aff *
3292 isl_union_pw_aff_from_pw_aff(
3293 __isl_take isl_pw_aff *pa);
3294 __isl_give isl_union_pw_multi_aff *
3295 isl_union_pw_multi_aff_from_aff(
3296 __isl_take isl_aff *aff);
3297 __isl_give isl_union_pw_multi_aff *
3298 isl_union_pw_multi_aff_from_pw_multi_aff(
3299 __isl_take isl_pw_multi_aff *pma);
3301 #include <isl/polynomial.h>
3302 __isl_give isl_union_pw_qpolynomial *
3303 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3304 __isl_take isl_pw_qpolynomial *pwqp);
3306 The following functions create a base expression on each
3307 of the sets in the union set and collect the results.
3309 #include <isl/aff.h>
3310 __isl_give isl_union_pw_multi_aff *
3311 isl_union_pw_multi_aff_from_union_pw_aff(
3312 __isl_take isl_union_pw_aff *upa);
3313 __isl_give isl_union_pw_aff *
3314 isl_union_pw_multi_aff_get_union_pw_aff(
3315 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3316 __isl_give isl_union_pw_aff *
3317 isl_union_pw_aff_val_on_domain(
3318 __isl_take isl_union_set *domain,
3319 __isl_take isl_val *v);
3320 __isl_give isl_union_pw_multi_aff *
3321 isl_union_pw_multi_aff_multi_val_on_domain(
3322 __isl_take isl_union_set *domain,
3323 __isl_take isl_multi_val *mv);
3324 __isl_give isl_union_pw_aff *
3325 isl_union_pw_aff_param_on_domain_id(
3326 __isl_take isl_union_set *domain,
3327 __isl_take isl_id *id);
3329 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3330 is the identifier of a parameter that may or may not already
3331 be present in C<domain>.
3333 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3335 expression on a given domain can be created using the following
3338 #include <isl/aff.h>
3339 __isl_give isl_union_pw_aff *
3340 isl_union_pw_aff_aff_on_domain(
3341 __isl_take isl_union_set *domain,
3342 __isl_take isl_aff *aff);
3343 __isl_give isl_union_pw_aff *
3344 isl_union_pw_aff_pw_aff_on_domain(
3345 __isl_take isl_union_set *domain,
3346 __isl_take isl_pw_aff *pa);
3348 A base expression can be added to a union expression using
3349 the following functions.
3351 #include <isl/aff.h>
3352 __isl_give isl_union_pw_aff *
3353 isl_union_pw_aff_add_pw_aff(
3354 __isl_take isl_union_pw_aff *upa,
3355 __isl_take isl_pw_aff *pa);
3356 __isl_give isl_union_pw_multi_aff *
3357 isl_union_pw_multi_aff_add_pw_multi_aff(
3358 __isl_take isl_union_pw_multi_aff *upma,
3359 __isl_take isl_pw_multi_aff *pma);
3361 #include <isl/polynomial.h>
3362 __isl_give isl_union_pw_qpolynomial *
3363 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3364 __isl_take isl_union_pw_qpolynomial *upwqp,
3365 __isl_take isl_pw_qpolynomial *pwqp);
3367 Union expressions can be copied and freed using
3368 the following functions.
3370 #include <isl/aff.h>
3371 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3372 __isl_keep isl_union_pw_aff *upa);
3373 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3374 __isl_take isl_union_pw_aff *upa);
3375 __isl_give isl_union_pw_multi_aff *
3376 isl_union_pw_multi_aff_copy(
3377 __isl_keep isl_union_pw_multi_aff *upma);
3378 __isl_null isl_union_pw_multi_aff *
3379 isl_union_pw_multi_aff_free(
3380 __isl_take isl_union_pw_multi_aff *upma);
3382 #include <isl/polynomial.h>
3383 __isl_give isl_union_pw_qpolynomial *
3384 isl_union_pw_qpolynomial_copy(
3385 __isl_keep isl_union_pw_qpolynomial *upwqp);
3386 __isl_null isl_union_pw_qpolynomial *
3387 isl_union_pw_qpolynomial_free(
3388 __isl_take isl_union_pw_qpolynomial *upwqp);
3389 __isl_give isl_union_pw_qpolynomial_fold *
3390 isl_union_pw_qpolynomial_fold_copy(
3391 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3392 __isl_null isl_union_pw_qpolynomial_fold *
3393 isl_union_pw_qpolynomial_fold_free(
3394 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3396 To iterate over the base expressions in a union expression,
3397 use the following functions.
3399 #include <isl/aff.h>
3400 int isl_union_pw_aff_n_pw_aff(
3401 __isl_keep isl_union_pw_aff *upa);
3402 isl_stat isl_union_pw_aff_foreach_pw_aff(
3403 __isl_keep isl_union_pw_aff *upa,
3404 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3405 void *user), void *user);
3406 int isl_union_pw_multi_aff_n_pw_multi_aff(
3407 __isl_keep isl_union_pw_multi_aff *upma);
3408 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3409 __isl_keep isl_union_pw_multi_aff *upma,
3410 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3411 void *user), void *user);
3413 #include <isl/polynomial.h>
3414 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3415 __isl_keep isl_union_pw_qpolynomial *upwqp);
3416 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3417 __isl_keep isl_union_pw_qpolynomial *upwqp,
3418 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3419 void *user), void *user);
3420 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3421 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3422 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3423 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3424 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3425 void *user), void *user);
3427 To extract the base expression in a given space from a union, use
3428 the following functions.
3430 #include <isl/aff.h>
3431 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3432 __isl_keep isl_union_pw_aff *upa,
3433 __isl_take isl_space *space);
3434 __isl_give isl_pw_multi_aff *
3435 isl_union_pw_multi_aff_extract_pw_multi_aff(
3436 __isl_keep isl_union_pw_multi_aff *upma,
3437 __isl_take isl_space *space);
3439 #include <isl/polynomial.h>
3440 __isl_give isl_pw_qpolynomial *
3441 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3442 __isl_keep isl_union_pw_qpolynomial *upwqp,
3443 __isl_take isl_space *space);
3445 =head2 Input and Output
3447 For set and relation,
3448 C<isl> supports its own input/output format, which is similar
3449 to the C<Omega> format, but also supports the C<PolyLib> format
3451 For other object types, typically only an C<isl> format is supported.
3453 =head3 C<isl> format
3455 The C<isl> format is similar to that of C<Omega>, but has a different
3456 syntax for describing the parameters and allows for the definition
3457 of an existentially quantified variable as the integer division
3458 of an affine expression.
3459 For example, the set of integers C<i> between C<0> and C<n>
3460 such that C<i % 10 <= 6> can be described as
3462 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3465 A set or relation can have several disjuncts, separated
3466 by the keyword C<or>. Each disjunct is either a conjunction
3467 of constraints or a projection (C<exists>) of a conjunction
3468 of constraints. The constraints are separated by the keyword
3471 =head3 C<PolyLib> format
3473 If the represented set is a union, then the first line
3474 contains a single number representing the number of disjuncts.
3475 Otherwise, a line containing the number C<1> is optional.
3477 Each disjunct is represented by a matrix of constraints.
3478 The first line contains two numbers representing
3479 the number of rows and columns,
3480 where the number of rows is equal to the number of constraints
3481 and the number of columns is equal to two plus the number of variables.
3482 The following lines contain the actual rows of the constraint matrix.
3483 In each row, the first column indicates whether the constraint
3484 is an equality (C<0>) or inequality (C<1>). The final column
3485 corresponds to the constant term.
3487 If the set is parametric, then the coefficients of the parameters
3488 appear in the last columns before the constant column.
3489 The coefficients of any existentially quantified variables appear
3490 between those of the set variables and those of the parameters.
3492 =head3 Extended C<PolyLib> format
3494 The extended C<PolyLib> format is nearly identical to the
3495 C<PolyLib> format. The only difference is that the line
3496 containing the number of rows and columns of a constraint matrix
3497 also contains four additional numbers:
3498 the number of output dimensions, the number of input dimensions,
3499 the number of local dimensions (i.e., the number of existentially
3500 quantified variables) and the number of parameters.
3501 For sets, the number of ``output'' dimensions is equal
3502 to the number of set dimensions, while the number of ``input''
3507 Objects can be read from input using the following functions.
3509 #include <isl/val.h>
3510 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3512 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3513 isl_ctx *ctx, const char *str);
3515 #include <isl/set.h>
3516 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3517 isl_ctx *ctx, FILE *input);
3518 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3519 isl_ctx *ctx, const char *str);
3520 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3522 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3525 #include <isl/map.h>
3526 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3527 isl_ctx *ctx, FILE *input);
3528 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3529 isl_ctx *ctx, const char *str);
3530 __isl_give isl_map *isl_map_read_from_file(
3531 isl_ctx *ctx, FILE *input);
3532 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3535 #include <isl/union_set.h>
3536 __isl_give isl_union_set *isl_union_set_read_from_file(
3537 isl_ctx *ctx, FILE *input);
3538 __isl_give isl_union_set *isl_union_set_read_from_str(
3539 isl_ctx *ctx, const char *str);
3541 #include <isl/union_map.h>
3542 __isl_give isl_union_map *isl_union_map_read_from_file(
3543 isl_ctx *ctx, FILE *input);
3544 __isl_give isl_union_map *isl_union_map_read_from_str(
3545 isl_ctx *ctx, const char *str);
3547 #include <isl/aff.h>
3548 __isl_give isl_aff *isl_aff_read_from_str(
3549 isl_ctx *ctx, const char *str);
3550 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3551 isl_ctx *ctx, const char *str);
3552 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3553 isl_ctx *ctx, const char *str);
3554 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3555 isl_ctx *ctx, const char *str);
3556 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3557 isl_ctx *ctx, const char *str);
3558 __isl_give isl_union_pw_aff *
3559 isl_union_pw_aff_read_from_str(
3560 isl_ctx *ctx, const char *str);
3561 __isl_give isl_union_pw_multi_aff *
3562 isl_union_pw_multi_aff_read_from_str(
3563 isl_ctx *ctx, const char *str);
3564 __isl_give isl_multi_union_pw_aff *
3565 isl_multi_union_pw_aff_read_from_str(
3566 isl_ctx *ctx, const char *str);
3568 #include <isl/polynomial.h>
3569 __isl_give isl_union_pw_qpolynomial *
3570 isl_union_pw_qpolynomial_read_from_str(
3571 isl_ctx *ctx, const char *str);
3573 For sets and relations,
3574 the input format is autodetected and may be either the C<PolyLib> format
3575 or the C<isl> format.
3579 Before anything can be printed, an C<isl_printer> needs to
3582 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3584 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3585 __isl_null isl_printer *isl_printer_free(
3586 __isl_take isl_printer *printer);
3588 C<isl_printer_to_file> prints to the given file, while
3589 C<isl_printer_to_str> prints to a string that can be extracted
3590 using the following function.
3592 #include <isl/printer.h>
3593 __isl_give char *isl_printer_get_str(
3594 __isl_keep isl_printer *printer);
3596 The printer can be inspected using the following functions.
3598 FILE *isl_printer_get_file(
3599 __isl_keep isl_printer *printer);
3600 int isl_printer_get_output_format(
3601 __isl_keep isl_printer *p);
3602 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3604 The behavior of the printer can be modified in various ways
3606 __isl_give isl_printer *isl_printer_set_output_format(
3607 __isl_take isl_printer *p, int output_format);
3608 __isl_give isl_printer *isl_printer_set_indent(
3609 __isl_take isl_printer *p, int indent);
3610 __isl_give isl_printer *isl_printer_set_indent_prefix(
3611 __isl_take isl_printer *p, const char *prefix);
3612 __isl_give isl_printer *isl_printer_indent(
3613 __isl_take isl_printer *p, int indent);
3614 __isl_give isl_printer *isl_printer_set_prefix(
3615 __isl_take isl_printer *p, const char *prefix);
3616 __isl_give isl_printer *isl_printer_set_suffix(
3617 __isl_take isl_printer *p, const char *suffix);
3618 __isl_give isl_printer *isl_printer_set_yaml_style(
3619 __isl_take isl_printer *p, int yaml_style);
3621 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3622 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3623 and defaults to C<ISL_FORMAT_ISL>.
3624 Each line in the output is prefixed by C<indent_prefix>,
3625 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3626 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3627 In the C<PolyLib> format output,
3628 the coefficients of the existentially quantified variables
3629 appear between those of the set variables and those
3631 The function C<isl_printer_indent> increases the indentation
3632 by the specified amount (which may be negative).
3633 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3634 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3637 To actually print something, use
3639 #include <isl/printer.h>
3640 __isl_give isl_printer *isl_printer_print_double(
3641 __isl_take isl_printer *p, double d);
3643 #include <isl/val.h>
3644 __isl_give isl_printer *isl_printer_print_val(
3645 __isl_take isl_printer *p, __isl_keep isl_val *v);
3647 #include <isl/set.h>
3648 __isl_give isl_printer *isl_printer_print_basic_set(
3649 __isl_take isl_printer *printer,
3650 __isl_keep isl_basic_set *bset);
3651 __isl_give isl_printer *isl_printer_print_set(
3652 __isl_take isl_printer *printer,
3653 __isl_keep isl_set *set);
3655 #include <isl/map.h>
3656 __isl_give isl_printer *isl_printer_print_basic_map(
3657 __isl_take isl_printer *printer,
3658 __isl_keep isl_basic_map *bmap);
3659 __isl_give isl_printer *isl_printer_print_map(
3660 __isl_take isl_printer *printer,
3661 __isl_keep isl_map *map);
3663 #include <isl/union_set.h>
3664 __isl_give isl_printer *isl_printer_print_union_set(
3665 __isl_take isl_printer *p,
3666 __isl_keep isl_union_set *uset);
3668 #include <isl/union_map.h>
3669 __isl_give isl_printer *isl_printer_print_union_map(
3670 __isl_take isl_printer *p,
3671 __isl_keep isl_union_map *umap);
3673 #include <isl/val.h>
3674 __isl_give isl_printer *isl_printer_print_multi_val(
3675 __isl_take isl_printer *p,
3676 __isl_keep isl_multi_val *mv);
3678 #include <isl/aff.h>
3679 __isl_give isl_printer *isl_printer_print_aff(
3680 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3681 __isl_give isl_printer *isl_printer_print_multi_aff(
3682 __isl_take isl_printer *p,
3683 __isl_keep isl_multi_aff *maff);
3684 __isl_give isl_printer *isl_printer_print_pw_aff(
3685 __isl_take isl_printer *p,
3686 __isl_keep isl_pw_aff *pwaff);
3687 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3688 __isl_take isl_printer *p,
3689 __isl_keep isl_pw_multi_aff *pma);
3690 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3691 __isl_take isl_printer *p,
3692 __isl_keep isl_multi_pw_aff *mpa);
3693 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3694 __isl_take isl_printer *p,
3695 __isl_keep isl_union_pw_aff *upa);
3696 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3697 __isl_take isl_printer *p,
3698 __isl_keep isl_union_pw_multi_aff *upma);
3699 __isl_give isl_printer *
3700 isl_printer_print_multi_union_pw_aff(
3701 __isl_take isl_printer *p,
3702 __isl_keep isl_multi_union_pw_aff *mupa);
3704 #include <isl/polynomial.h>
3705 __isl_give isl_printer *isl_printer_print_qpolynomial(
3706 __isl_take isl_printer *p,
3707 __isl_keep isl_qpolynomial *qp);
3708 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3709 __isl_take isl_printer *p,
3710 __isl_keep isl_pw_qpolynomial *pwqp);
3711 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3712 __isl_take isl_printer *p,
3713 __isl_keep isl_union_pw_qpolynomial *upwqp);
3715 __isl_give isl_printer *
3716 isl_printer_print_pw_qpolynomial_fold(
3717 __isl_take isl_printer *p,
3718 __isl_keep isl_pw_qpolynomial_fold *pwf);
3719 __isl_give isl_printer *
3720 isl_printer_print_union_pw_qpolynomial_fold(
3721 __isl_take isl_printer *p,
3722 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3724 For C<isl_printer_print_qpolynomial>,
3725 C<isl_printer_print_pw_qpolynomial> and
3726 C<isl_printer_print_pw_qpolynomial_fold>,
3727 the output format of the printer
3728 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3729 For C<isl_printer_print_union_pw_qpolynomial> and
3730 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3732 In case of printing in C<ISL_FORMAT_C>, the user may want
3733 to set the names of all dimensions first.
3735 C<isl> also provides limited support for printing YAML documents,
3736 just enough for the internal use for printing such documents.
3738 #include <isl/printer.h>
3739 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3740 __isl_take isl_printer *p);
3741 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3742 __isl_take isl_printer *p);
3743 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3744 __isl_take isl_printer *p);
3745 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3746 __isl_take isl_printer *p);
3747 __isl_give isl_printer *isl_printer_yaml_next(
3748 __isl_take isl_printer *p);
3750 A document is started by a call to either
3751 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3752 Anything printed to the printer after such a call belong to the
3753 first key of the mapping or the first element in the sequence.
3754 The function C<isl_printer_yaml_next> moves to the value if
3755 we are currently printing a mapping key, the next key if we
3756 are printing a value or the next element if we are printing
3757 an element in a sequence.
3758 Nested mappings and sequences are initiated by the same
3759 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3760 Each call to these functions needs to have a corresponding call to
3761 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3763 When called on a file printer, the following function flushes
3764 the file. When called on a string printer, the buffer is cleared.
3766 __isl_give isl_printer *isl_printer_flush(
3767 __isl_take isl_printer *p);
3769 The following functions allow the user to attach
3770 notes to a printer in order to keep track of additional state.
3772 #include <isl/printer.h>
3773 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3774 __isl_keep isl_id *id);
3775 __isl_give isl_id *isl_printer_get_note(
3776 __isl_keep isl_printer *p, __isl_take isl_id *id);
3777 __isl_give isl_printer *isl_printer_set_note(
3778 __isl_take isl_printer *p,
3779 __isl_take isl_id *id, __isl_take isl_id *note);
3781 C<isl_printer_set_note> associates the given note to the given
3782 identifier in the printer.
3783 C<isl_printer_get_note> retrieves a note associated to an
3785 C<isl_printer_has_note> checks if there is such a note.
3786 C<isl_printer_get_note> fails if the requested note does not exist.
3788 Alternatively, a string representation can be obtained
3789 directly using the following functions, which always print
3793 __isl_give char *isl_id_to_str(
3794 __isl_keep isl_id *id);
3796 #include <isl/space.h>
3797 __isl_give char *isl_space_to_str(
3798 __isl_keep isl_space *space);
3800 #include <isl/val.h>
3801 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3802 __isl_give char *isl_multi_val_to_str(
3803 __isl_keep isl_multi_val *mv);
3805 #include <isl/set.h>
3806 __isl_give char *isl_basic_set_to_str(
3807 __isl_keep isl_basic_set *bset);
3808 __isl_give char *isl_set_to_str(
3809 __isl_keep isl_set *set);
3811 #include <isl/union_set.h>
3812 __isl_give char *isl_union_set_to_str(
3813 __isl_keep isl_union_set *uset);
3815 #include <isl/map.h>
3816 __isl_give char *isl_basic_map_to_str(
3817 __isl_keep isl_basic_map *bmap);
3818 __isl_give char *isl_map_to_str(
3819 __isl_keep isl_map *map);
3821 #include <isl/union_map.h>
3822 __isl_give char *isl_union_map_to_str(
3823 __isl_keep isl_union_map *umap);
3825 #include <isl/aff.h>
3826 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3827 __isl_give char *isl_pw_aff_to_str(
3828 __isl_keep isl_pw_aff *pa);
3829 __isl_give char *isl_multi_aff_to_str(
3830 __isl_keep isl_multi_aff *ma);
3831 __isl_give char *isl_pw_multi_aff_to_str(
3832 __isl_keep isl_pw_multi_aff *pma);
3833 __isl_give char *isl_multi_pw_aff_to_str(
3834 __isl_keep isl_multi_pw_aff *mpa);
3835 __isl_give char *isl_union_pw_aff_to_str(
3836 __isl_keep isl_union_pw_aff *upa);
3837 __isl_give char *isl_union_pw_multi_aff_to_str(
3838 __isl_keep isl_union_pw_multi_aff *upma);
3839 __isl_give char *isl_multi_union_pw_aff_to_str(
3840 __isl_keep isl_multi_union_pw_aff *mupa);
3842 #include <isl/point.h>
3843 __isl_give char *isl_point_to_str(
3844 __isl_keep isl_point *pnt);
3846 #include <isl/polynomial.h>
3847 __isl_give char *isl_pw_qpolynomial_to_str(
3848 __isl_keep isl_pw_qpolynomial *pwqp);
3849 __isl_give char *isl_union_pw_qpolynomial_to_str(
3850 __isl_keep isl_union_pw_qpolynomial *upwqp);
3854 =head3 Unary Properties
3860 The following functions test whether the given set or relation
3861 contains any integer points. The ``plain'' variants do not perform
3862 any computations, but simply check if the given set or relation
3863 is already known to be empty.
3865 #include <isl/set.h>
3866 isl_bool isl_basic_set_plain_is_empty(
3867 __isl_keep isl_basic_set *bset);
3868 isl_bool isl_basic_set_is_empty(
3869 __isl_keep isl_basic_set *bset);
3870 isl_bool isl_set_plain_is_empty(
3871 __isl_keep isl_set *set);
3872 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3874 #include <isl/union_set.h>
3875 isl_bool isl_union_set_is_empty(
3876 __isl_keep isl_union_set *uset);
3878 #include <isl/map.h>
3879 isl_bool isl_basic_map_plain_is_empty(
3880 __isl_keep isl_basic_map *bmap);
3881 isl_bool isl_basic_map_is_empty(
3882 __isl_keep isl_basic_map *bmap);
3883 isl_bool isl_map_plain_is_empty(
3884 __isl_keep isl_map *map);
3885 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3887 #include <isl/union_map.h>
3888 isl_bool isl_union_map_plain_is_empty(
3889 __isl_keep isl_union_map *umap);
3890 isl_bool isl_union_map_is_empty(
3891 __isl_keep isl_union_map *umap);
3893 =item * Universality
3895 isl_bool isl_basic_set_plain_is_universe(
3896 __isl_keep isl_basic_set *bset);
3897 isl_bool isl_basic_set_is_universe(
3898 __isl_keep isl_basic_set *bset);
3899 isl_bool isl_basic_map_plain_is_universe(
3900 __isl_keep isl_basic_map *bmap);
3901 isl_bool isl_basic_map_is_universe(
3902 __isl_keep isl_basic_map *bmap);
3903 isl_bool isl_set_plain_is_universe(
3904 __isl_keep isl_set *set);
3905 isl_bool isl_map_plain_is_universe(
3906 __isl_keep isl_map *map);
3908 =item * Single-valuedness
3910 #include <isl/set.h>
3911 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3913 #include <isl/map.h>
3914 isl_bool isl_basic_map_is_single_valued(
3915 __isl_keep isl_basic_map *bmap);
3916 isl_bool isl_map_plain_is_single_valued(
3917 __isl_keep isl_map *map);
3918 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3920 #include <isl/union_map.h>
3921 isl_bool isl_union_map_is_single_valued(
3922 __isl_keep isl_union_map *umap);
3926 isl_bool isl_map_plain_is_injective(
3927 __isl_keep isl_map *map);
3928 isl_bool isl_map_is_injective(
3929 __isl_keep isl_map *map);
3930 isl_bool isl_union_map_plain_is_injective(
3931 __isl_keep isl_union_map *umap);
3932 isl_bool isl_union_map_is_injective(
3933 __isl_keep isl_union_map *umap);
3937 isl_bool isl_map_is_bijective(
3938 __isl_keep isl_map *map);
3939 isl_bool isl_union_map_is_bijective(
3940 __isl_keep isl_union_map *umap);
3944 The following functions test whether the given relation
3945 only maps elements to themselves.
3947 #include <isl/map.h>
3948 isl_bool isl_map_is_identity(
3949 __isl_keep isl_map *map);
3951 #include <isl/union_map.h>
3952 isl_bool isl_union_map_is_identity(
3953 __isl_keep isl_union_map *umap);
3957 __isl_give isl_val *
3958 isl_basic_map_plain_get_val_if_fixed(
3959 __isl_keep isl_basic_map *bmap,
3960 enum isl_dim_type type, unsigned pos);
3961 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3962 __isl_keep isl_set *set,
3963 enum isl_dim_type type, unsigned pos);
3964 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3965 __isl_keep isl_map *map,
3966 enum isl_dim_type type, unsigned pos);
3968 If the set or relation obviously lies on a hyperplane where the given dimension
3969 has a fixed value, then return that value.
3970 Otherwise return NaN.
3974 isl_stat isl_set_dim_residue_class_val(
3975 __isl_keep isl_set *set,
3976 int pos, __isl_give isl_val **modulo,
3977 __isl_give isl_val **residue);
3979 Check if the values of the given set dimension are equal to a fixed
3980 value modulo some integer value. If so, assign the modulo to C<*modulo>
3981 and the fixed value to C<*residue>. If the given dimension attains only
3982 a single value, then assign C<0> to C<*modulo> and the fixed value to
3984 If the dimension does not attain only a single value and if no modulo
3985 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3987 #include <isl/set.h>
3988 __isl_give isl_stride_info *isl_set_get_stride_info(
3989 __isl_keep isl_set *set, int pos);
3990 __isl_give isl_val *isl_set_get_stride(
3991 __isl_keep isl_set *set, int pos);
3993 #include <isl/map.h>
3994 __isl_give isl_stride_info *
3995 isl_map_get_range_stride_info(
3996 __isl_keep isl_map *map, int pos);
3998 Check if the values of the given set dimension are equal to
3999 some affine expression of the other dimensions (the offset)
4000 modulo some integer stride or
4001 check if the values of the given output dimensions are equal to
4002 some affine expression of the input dimensions (the offset)
4003 modulo some integer stride.
4004 If no more specific information can be found, then the stride
4005 is taken to be one and the offset is taken to be the zero expression.
4006 The function C<isl_set_get_stride> performs the same
4007 computation as C<isl_set_get_stride_info> but only returns the stride.
4008 For the other functions,
4009 the stride and offset can be extracted from the returned object
4010 using the following functions.
4012 #include <isl/stride_info.h>
4013 __isl_give isl_val *isl_stride_info_get_stride(
4014 __isl_keep isl_stride_info *si);
4015 __isl_give isl_aff *isl_stride_info_get_offset(
4016 __isl_keep isl_stride_info *si);
4018 The stride info object can be released using the following function.
4020 #include <isl/stride_info.h>
4021 __isl_null isl_stride_info *isl_stride_info_free(
4022 __isl_take isl_stride_info *si);
4026 To check whether the description of a set, relation or function depends
4027 on one or more given dimensions,
4028 the following functions can be used.
4030 #include <isl/constraint.h>
4031 isl_bool isl_constraint_involves_dims(
4032 __isl_keep isl_constraint *constraint,
4033 enum isl_dim_type type, unsigned first, unsigned n);
4035 #include <isl/set.h>
4036 isl_bool isl_basic_set_involves_dims(
4037 __isl_keep isl_basic_set *bset,
4038 enum isl_dim_type type, unsigned first, unsigned n);
4039 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4040 enum isl_dim_type type, unsigned first, unsigned n);
4042 #include <isl/map.h>
4043 isl_bool isl_basic_map_involves_dims(
4044 __isl_keep isl_basic_map *bmap,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4046 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4047 enum isl_dim_type type, unsigned first, unsigned n);
4049 #include <isl/union_map.h>
4050 isl_bool isl_union_map_involves_dims(
4051 __isl_keep isl_union_map *umap,
4052 enum isl_dim_type type, unsigned first, unsigned n);
4054 #include <isl/aff.h>
4055 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4056 enum isl_dim_type type, unsigned first, unsigned n);
4057 isl_bool isl_pw_aff_involves_dims(
4058 __isl_keep isl_pw_aff *pwaff,
4059 enum isl_dim_type type, unsigned first, unsigned n);
4060 isl_bool isl_multi_aff_involves_dims(
4061 __isl_keep isl_multi_aff *ma,
4062 enum isl_dim_type type, unsigned first, unsigned n);
4063 isl_bool isl_pw_multi_aff_involves_dims(
4064 __isl_keep isl_pw_multi_aff *pma,
4065 enum isl_dim_type type, unsigned first, unsigned n);
4066 isl_bool isl_multi_pw_aff_involves_dims(
4067 __isl_keep isl_multi_pw_aff *mpa,
4068 enum isl_dim_type type, unsigned first, unsigned n);
4070 #include <isl/polynomial.h>
4071 isl_bool isl_qpolynomial_involves_dims(
4072 __isl_keep isl_qpolynomial *qp,
4073 enum isl_dim_type type, unsigned first, unsigned n);
4075 Similarly, the following functions can be used to check whether
4076 a given dimension is involved in any lower or upper bound.
4078 #include <isl/set.h>
4079 isl_bool isl_set_dim_has_any_lower_bound(
4080 __isl_keep isl_set *set,
4081 enum isl_dim_type type, unsigned pos);
4082 isl_bool isl_set_dim_has_any_upper_bound(
4083 __isl_keep isl_set *set,
4084 enum isl_dim_type type, unsigned pos);
4086 Note that these functions return true even if there is a bound on
4087 the dimension on only some of the basic sets of C<set>.
4088 To check if they have a bound for all of the basic sets in C<set>,
4089 use the following functions instead.
4091 #include <isl/set.h>
4092 isl_bool isl_set_dim_has_lower_bound(
4093 __isl_keep isl_set *set,
4094 enum isl_dim_type type, unsigned pos);
4095 isl_bool isl_set_dim_has_upper_bound(
4096 __isl_keep isl_set *set,
4097 enum isl_dim_type type, unsigned pos);
4101 To check whether a set is a parameter domain, use this function:
4103 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4104 isl_bool isl_union_set_is_params(
4105 __isl_keep isl_union_set *uset);
4109 The following functions check whether the space of the given
4110 (basic) set or relation domain and/or range is a wrapped relation.
4112 #include <isl/space.h>
4113 isl_bool isl_space_is_wrapping(
4114 __isl_keep isl_space *space);
4115 isl_bool isl_space_domain_is_wrapping(
4116 __isl_keep isl_space *space);
4117 isl_bool isl_space_range_is_wrapping(
4118 __isl_keep isl_space *space);
4119 isl_bool isl_space_is_product(
4120 __isl_keep isl_space *space);
4122 #include <isl/set.h>
4123 isl_bool isl_basic_set_is_wrapping(
4124 __isl_keep isl_basic_set *bset);
4125 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4127 #include <isl/map.h>
4128 isl_bool isl_map_domain_is_wrapping(
4129 __isl_keep isl_map *map);
4130 isl_bool isl_map_range_is_wrapping(
4131 __isl_keep isl_map *map);
4132 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4134 #include <isl/val.h>
4135 isl_bool isl_multi_val_range_is_wrapping(
4136 __isl_keep isl_multi_val *mv);
4138 #include <isl/aff.h>
4139 isl_bool isl_multi_aff_range_is_wrapping(
4140 __isl_keep isl_multi_aff *ma);
4141 isl_bool isl_multi_pw_aff_range_is_wrapping(
4142 __isl_keep isl_multi_pw_aff *mpa);
4143 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4144 __isl_keep isl_multi_union_pw_aff *mupa);
4146 The input to C<isl_space_is_wrapping> should
4147 be the space of a set, while that of
4148 C<isl_space_domain_is_wrapping> and
4149 C<isl_space_range_is_wrapping> should be the space of a relation.
4150 The input to C<isl_space_is_product> can be either the space
4151 of a set or that of a binary relation.
4152 In case the input is the space of a binary relation, it checks
4153 whether both domain and range are wrapping.
4155 =item * Internal Product
4157 isl_bool isl_basic_map_can_zip(
4158 __isl_keep isl_basic_map *bmap);
4159 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4161 Check whether the product of domain and range of the given relation
4163 i.e., whether both domain and range are nested relations.
4167 #include <isl/space.h>
4168 isl_bool isl_space_can_curry(
4169 __isl_keep isl_space *space);
4171 #include <isl/map.h>
4172 isl_bool isl_basic_map_can_curry(
4173 __isl_keep isl_basic_map *bmap);
4174 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4176 Check whether the domain of the (basic) relation is a wrapped relation.
4178 #include <isl/space.h>
4179 __isl_give isl_space *isl_space_uncurry(
4180 __isl_take isl_space *space);
4182 #include <isl/map.h>
4183 isl_bool isl_basic_map_can_uncurry(
4184 __isl_keep isl_basic_map *bmap);
4185 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4187 Check whether the range of the (basic) relation is a wrapped relation.
4189 #include <isl/space.h>
4190 isl_bool isl_space_can_range_curry(
4191 __isl_keep isl_space *space);
4193 #include <isl/map.h>
4194 isl_bool isl_map_can_range_curry(
4195 __isl_keep isl_map *map);
4197 Check whether the domain of the relation wrapped in the range of
4198 the input is itself a wrapped relation.
4200 =item * Special Values
4202 #include <isl/aff.h>
4203 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4204 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4205 isl_bool isl_multi_pw_aff_is_cst(
4206 __isl_keep isl_multi_pw_aff *mpa);
4208 Check whether the given expression is a constant.
4210 #include <isl/val.h>
4211 isl_bool isl_multi_val_involves_nan(
4212 __isl_keep isl_multi_val *mv);
4214 #include <isl/aff.h>
4215 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4216 isl_bool isl_multi_aff_involves_nan(
4217 __isl_keep isl_multi_aff *ma);
4218 isl_bool isl_pw_aff_involves_nan(
4219 __isl_keep isl_pw_aff *pa);
4220 isl_bool isl_pw_multi_aff_involves_nan(
4221 __isl_keep isl_pw_multi_aff *pma);
4222 isl_bool isl_multi_pw_aff_involves_nan(
4223 __isl_keep isl_multi_pw_aff *mpa);
4224 isl_bool isl_union_pw_aff_involves_nan(
4225 __isl_keep isl_union_pw_aff *upa);
4226 isl_bool isl_union_pw_multi_aff_involves_nan(
4227 __isl_keep isl_union_pw_multi_aff *upma);
4228 isl_bool isl_multi_union_pw_aff_involves_nan(
4229 __isl_keep isl_multi_union_pw_aff *mupa);
4231 #include <isl/polynomial.h>
4232 isl_bool isl_qpolynomial_is_nan(
4233 __isl_keep isl_qpolynomial *qp);
4234 isl_bool isl_qpolynomial_fold_is_nan(
4235 __isl_keep isl_qpolynomial_fold *fold);
4236 isl_bool isl_pw_qpolynomial_involves_nan(
4237 __isl_keep isl_pw_qpolynomial *pwqp);
4238 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4239 __isl_keep isl_pw_qpolynomial_fold *pwf);
4240 isl_bool isl_union_pw_qpolynomial_involves_nan(
4241 __isl_keep isl_union_pw_qpolynomial *upwqp);
4242 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4243 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4245 Check whether the given expression is equal to or involves NaN.
4247 #include <isl/aff.h>
4248 isl_bool isl_aff_plain_is_zero(
4249 __isl_keep isl_aff *aff);
4251 Check whether the affine expression is obviously zero.
4255 =head3 Binary Properties
4261 The following functions check whether two objects
4262 represent the same set, relation or function.
4263 The C<plain> variants only return true if the objects
4264 are obviously the same. That is, they may return false
4265 even if the objects are the same, but they will never
4266 return true if the objects are not the same.
4268 #include <isl/set.h>
4269 isl_bool isl_basic_set_plain_is_equal(
4270 __isl_keep isl_basic_set *bset1,
4271 __isl_keep isl_basic_set *bset2);
4272 isl_bool isl_basic_set_is_equal(
4273 __isl_keep isl_basic_set *bset1,
4274 __isl_keep isl_basic_set *bset2);
4275 isl_bool isl_set_plain_is_equal(
4276 __isl_keep isl_set *set1,
4277 __isl_keep isl_set *set2);
4278 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4279 __isl_keep isl_set *set2);
4281 #include <isl/map.h>
4282 isl_bool isl_basic_map_is_equal(
4283 __isl_keep isl_basic_map *bmap1,
4284 __isl_keep isl_basic_map *bmap2);
4285 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4286 __isl_keep isl_map *map2);
4287 isl_bool isl_map_plain_is_equal(
4288 __isl_keep isl_map *map1,
4289 __isl_keep isl_map *map2);
4291 #include <isl/union_set.h>
4292 isl_bool isl_union_set_is_equal(
4293 __isl_keep isl_union_set *uset1,
4294 __isl_keep isl_union_set *uset2);
4296 #include <isl/union_map.h>
4297 isl_bool isl_union_map_is_equal(
4298 __isl_keep isl_union_map *umap1,
4299 __isl_keep isl_union_map *umap2);
4301 #include <isl/aff.h>
4302 isl_bool isl_aff_plain_is_equal(
4303 __isl_keep isl_aff *aff1,
4304 __isl_keep isl_aff *aff2);
4305 isl_bool isl_multi_aff_plain_is_equal(
4306 __isl_keep isl_multi_aff *maff1,
4307 __isl_keep isl_multi_aff *maff2);
4308 isl_bool isl_pw_aff_plain_is_equal(
4309 __isl_keep isl_pw_aff *pwaff1,
4310 __isl_keep isl_pw_aff *pwaff2);
4311 isl_bool isl_pw_aff_is_equal(
4312 __isl_keep isl_pw_aff *pa1,
4313 __isl_keep isl_pw_aff *pa2);
4314 isl_bool isl_pw_multi_aff_plain_is_equal(
4315 __isl_keep isl_pw_multi_aff *pma1,
4316 __isl_keep isl_pw_multi_aff *pma2);
4317 isl_bool isl_pw_multi_aff_is_equal(
4318 __isl_keep isl_pw_multi_aff *pma1,
4319 __isl_keep isl_pw_multi_aff *pma2);
4320 isl_bool isl_multi_pw_aff_plain_is_equal(
4321 __isl_keep isl_multi_pw_aff *mpa1,
4322 __isl_keep isl_multi_pw_aff *mpa2);
4323 isl_bool isl_multi_pw_aff_is_equal(
4324 __isl_keep isl_multi_pw_aff *mpa1,
4325 __isl_keep isl_multi_pw_aff *mpa2);
4326 isl_bool isl_union_pw_aff_plain_is_equal(
4327 __isl_keep isl_union_pw_aff *upa1,
4328 __isl_keep isl_union_pw_aff *upa2);
4329 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4330 __isl_keep isl_union_pw_multi_aff *upma1,
4331 __isl_keep isl_union_pw_multi_aff *upma2);
4332 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4333 __isl_keep isl_multi_union_pw_aff *mupa1,
4334 __isl_keep isl_multi_union_pw_aff *mupa2);
4336 #include <isl/polynomial.h>
4337 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4338 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4339 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4340 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4341 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4342 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4344 =item * Disjointness
4346 #include <isl/set.h>
4347 isl_bool isl_basic_set_is_disjoint(
4348 __isl_keep isl_basic_set *bset1,
4349 __isl_keep isl_basic_set *bset2);
4350 isl_bool isl_set_plain_is_disjoint(
4351 __isl_keep isl_set *set1,
4352 __isl_keep isl_set *set2);
4353 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4354 __isl_keep isl_set *set2);
4356 #include <isl/map.h>
4357 isl_bool isl_basic_map_is_disjoint(
4358 __isl_keep isl_basic_map *bmap1,
4359 __isl_keep isl_basic_map *bmap2);
4360 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4361 __isl_keep isl_map *map2);
4363 #include <isl/union_set.h>
4364 isl_bool isl_union_set_is_disjoint(
4365 __isl_keep isl_union_set *uset1,
4366 __isl_keep isl_union_set *uset2);
4368 #include <isl/union_map.h>
4369 isl_bool isl_union_map_is_disjoint(
4370 __isl_keep isl_union_map *umap1,
4371 __isl_keep isl_union_map *umap2);
4375 isl_bool isl_basic_set_is_subset(
4376 __isl_keep isl_basic_set *bset1,
4377 __isl_keep isl_basic_set *bset2);
4378 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4379 __isl_keep isl_set *set2);
4380 isl_bool isl_set_is_strict_subset(
4381 __isl_keep isl_set *set1,
4382 __isl_keep isl_set *set2);
4383 isl_bool isl_union_set_is_subset(
4384 __isl_keep isl_union_set *uset1,
4385 __isl_keep isl_union_set *uset2);
4386 isl_bool isl_union_set_is_strict_subset(
4387 __isl_keep isl_union_set *uset1,
4388 __isl_keep isl_union_set *uset2);
4389 isl_bool isl_basic_map_is_subset(
4390 __isl_keep isl_basic_map *bmap1,
4391 __isl_keep isl_basic_map *bmap2);
4392 isl_bool isl_basic_map_is_strict_subset(
4393 __isl_keep isl_basic_map *bmap1,
4394 __isl_keep isl_basic_map *bmap2);
4395 isl_bool isl_map_is_subset(
4396 __isl_keep isl_map *map1,
4397 __isl_keep isl_map *map2);
4398 isl_bool isl_map_is_strict_subset(
4399 __isl_keep isl_map *map1,
4400 __isl_keep isl_map *map2);
4401 isl_bool isl_union_map_is_subset(
4402 __isl_keep isl_union_map *umap1,
4403 __isl_keep isl_union_map *umap2);
4404 isl_bool isl_union_map_is_strict_subset(
4405 __isl_keep isl_union_map *umap1,
4406 __isl_keep isl_union_map *umap2);
4408 Check whether the first argument is a (strict) subset of the
4413 Every comparison function returns a negative value if the first
4414 argument is considered smaller than the second, a positive value
4415 if the first argument is considered greater and zero if the two
4416 constraints are considered the same by the comparison criterion.
4418 #include <isl/constraint.h>
4419 int isl_constraint_plain_cmp(
4420 __isl_keep isl_constraint *c1,
4421 __isl_keep isl_constraint *c2);
4423 This function is useful for sorting C<isl_constraint>s.
4424 The order depends on the internal representation of the inputs.
4425 The order is fixed over different calls to the function (assuming
4426 the internal representation of the inputs has not changed), but may
4427 change over different versions of C<isl>.
4429 #include <isl/constraint.h>
4430 int isl_constraint_cmp_last_non_zero(
4431 __isl_keep isl_constraint *c1,
4432 __isl_keep isl_constraint *c2);
4434 This function can be used to sort constraints that live in the same
4435 local space. Constraints that involve ``earlier'' dimensions or
4436 that have a smaller coefficient for the shared latest dimension
4437 are considered smaller than other constraints.
4438 This function only defines a B<partial> order.
4440 #include <isl/set.h>
4441 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4442 __isl_keep isl_set *set2);
4444 This function is useful for sorting C<isl_set>s.
4445 The order depends on the internal representation of the inputs.
4446 The order is fixed over different calls to the function (assuming
4447 the internal representation of the inputs has not changed), but may
4448 change over different versions of C<isl>.
4450 #include <isl/aff.h>
4451 int isl_multi_aff_plain_cmp(
4452 __isl_keep isl_multi_aff *ma1,
4453 __isl_keep isl_multi_aff *ma2);
4454 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4455 __isl_keep isl_pw_aff *pa2);
4457 The functions C<isl_multi_aff_plain_cmp> and
4458 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4459 C<isl_pw_aff>s. The order is not strictly defined.
4460 The current order sorts expressions that only involve
4461 earlier dimensions before those that involve later dimensions.
4465 =head2 Unary Operations
4471 __isl_give isl_set *isl_set_complement(
4472 __isl_take isl_set *set);
4473 __isl_give isl_map *isl_map_complement(
4474 __isl_take isl_map *map);
4478 #include <isl/space.h>
4479 __isl_give isl_space *isl_space_reverse(
4480 __isl_take isl_space *space);
4482 #include <isl/map.h>
4483 __isl_give isl_basic_map *isl_basic_map_reverse(
4484 __isl_take isl_basic_map *bmap);
4485 __isl_give isl_map *isl_map_reverse(
4486 __isl_take isl_map *map);
4488 #include <isl/union_map.h>
4489 __isl_give isl_union_map *isl_union_map_reverse(
4490 __isl_take isl_union_map *umap);
4494 #include <isl/space.h>
4495 __isl_give isl_space *isl_space_domain(
4496 __isl_take isl_space *space);
4497 __isl_give isl_space *isl_space_range(
4498 __isl_take isl_space *space);
4499 __isl_give isl_space *isl_space_params(
4500 __isl_take isl_space *space);
4502 #include <isl/local_space.h>
4503 __isl_give isl_local_space *isl_local_space_domain(
4504 __isl_take isl_local_space *ls);
4505 __isl_give isl_local_space *isl_local_space_range(
4506 __isl_take isl_local_space *ls);
4508 #include <isl/set.h>
4509 __isl_give isl_basic_set *isl_basic_set_project_out(
4510 __isl_take isl_basic_set *bset,
4511 enum isl_dim_type type, unsigned first, unsigned n);
4512 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4513 enum isl_dim_type type, unsigned first, unsigned n);
4514 __isl_give isl_map *isl_set_project_onto_map(
4515 __isl_take isl_set *set,
4516 enum isl_dim_type type, unsigned first,
4518 __isl_give isl_basic_set *isl_basic_set_params(
4519 __isl_take isl_basic_set *bset);
4520 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4522 The function C<isl_set_project_onto_map> returns a relation
4523 that projects the input set onto the given set dimensions.
4525 #include <isl/map.h>
4526 __isl_give isl_basic_map *isl_basic_map_project_out(
4527 __isl_take isl_basic_map *bmap,
4528 enum isl_dim_type type, unsigned first, unsigned n);
4529 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4530 enum isl_dim_type type, unsigned first, unsigned n);
4531 __isl_give isl_basic_set *isl_basic_map_domain(
4532 __isl_take isl_basic_map *bmap);
4533 __isl_give isl_basic_set *isl_basic_map_range(
4534 __isl_take isl_basic_map *bmap);
4535 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4536 __isl_give isl_set *isl_map_domain(
4537 __isl_take isl_map *bmap);
4538 __isl_give isl_set *isl_map_range(
4539 __isl_take isl_map *map);
4541 #include <isl/union_set.h>
4542 __isl_give isl_union_set *isl_union_set_project_out(
4543 __isl_take isl_union_set *uset,
4544 enum isl_dim_type type,
4545 unsigned first, unsigned n);
4546 __isl_give isl_set *isl_union_set_params(
4547 __isl_take isl_union_set *uset);
4549 The function C<isl_union_set_project_out> can only project out
4552 #include <isl/union_map.h>
4553 __isl_give isl_union_map *isl_union_map_project_out(
4554 __isl_take isl_union_map *umap,
4555 enum isl_dim_type type, unsigned first, unsigned n);
4556 __isl_give isl_union_map *
4557 isl_union_map_project_out_all_params(
4558 __isl_take isl_union_map *umap);
4559 __isl_give isl_set *isl_union_map_params(
4560 __isl_take isl_union_map *umap);
4561 __isl_give isl_union_set *isl_union_map_domain(
4562 __isl_take isl_union_map *umap);
4563 __isl_give isl_union_set *isl_union_map_range(
4564 __isl_take isl_union_map *umap);
4566 The function C<isl_union_map_project_out> can only project out
4569 #include <isl/aff.h>
4570 __isl_give isl_aff *isl_aff_project_domain_on_params(
4571 __isl_take isl_aff *aff);
4572 __isl_give isl_multi_aff *
4573 isl_multi_aff_project_domain_on_params(
4574 __isl_take isl_multi_aff *ma);
4575 __isl_give isl_pw_aff *
4576 isl_pw_aff_project_domain_on_params(
4577 __isl_take isl_pw_aff *pa);
4578 __isl_give isl_multi_pw_aff *
4579 isl_multi_pw_aff_project_domain_on_params(
4580 __isl_take isl_multi_pw_aff *mpa);
4581 __isl_give isl_pw_multi_aff *
4582 isl_pw_multi_aff_project_domain_on_params(
4583 __isl_take isl_pw_multi_aff *pma);
4584 __isl_give isl_set *isl_pw_aff_domain(
4585 __isl_take isl_pw_aff *pwaff);
4586 __isl_give isl_set *isl_pw_multi_aff_domain(
4587 __isl_take isl_pw_multi_aff *pma);
4588 __isl_give isl_set *isl_multi_pw_aff_domain(
4589 __isl_take isl_multi_pw_aff *mpa);
4590 __isl_give isl_union_set *isl_union_pw_aff_domain(
4591 __isl_take isl_union_pw_aff *upa);
4592 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4593 __isl_take isl_union_pw_multi_aff *upma);
4594 __isl_give isl_union_set *
4595 isl_multi_union_pw_aff_domain(
4596 __isl_take isl_multi_union_pw_aff *mupa);
4597 __isl_give isl_set *isl_pw_aff_params(
4598 __isl_take isl_pw_aff *pwa);
4600 If no explicit domain was set on a zero-dimensional input to
4601 C<isl_multi_union_pw_aff_domain>, then this function will
4602 return a parameter set.
4604 #include <isl/polynomial.h>
4605 __isl_give isl_qpolynomial *
4606 isl_qpolynomial_project_domain_on_params(
4607 __isl_take isl_qpolynomial *qp);
4608 __isl_give isl_pw_qpolynomial *
4609 isl_pw_qpolynomial_project_domain_on_params(
4610 __isl_take isl_pw_qpolynomial *pwqp);
4611 __isl_give isl_pw_qpolynomial_fold *
4612 isl_pw_qpolynomial_fold_project_domain_on_params(
4613 __isl_take isl_pw_qpolynomial_fold *pwf);
4614 __isl_give isl_set *isl_pw_qpolynomial_domain(
4615 __isl_take isl_pw_qpolynomial *pwqp);
4616 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4617 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4618 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4619 __isl_take isl_union_pw_qpolynomial *upwqp);
4621 #include <isl/space.h>
4622 __isl_give isl_space *isl_space_domain_map(
4623 __isl_take isl_space *space);
4624 __isl_give isl_space *isl_space_range_map(
4625 __isl_take isl_space *space);
4627 #include <isl/map.h>
4628 __isl_give isl_map *isl_set_wrapped_domain_map(
4629 __isl_take isl_set *set);
4630 __isl_give isl_basic_map *isl_basic_map_domain_map(
4631 __isl_take isl_basic_map *bmap);
4632 __isl_give isl_basic_map *isl_basic_map_range_map(
4633 __isl_take isl_basic_map *bmap);
4634 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4635 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4637 #include <isl/union_map.h>
4638 __isl_give isl_union_map *isl_union_map_domain_map(
4639 __isl_take isl_union_map *umap);
4640 __isl_give isl_union_pw_multi_aff *
4641 isl_union_map_domain_map_union_pw_multi_aff(
4642 __isl_take isl_union_map *umap);
4643 __isl_give isl_union_map *isl_union_map_range_map(
4644 __isl_take isl_union_map *umap);
4645 __isl_give isl_union_map *
4646 isl_union_set_wrapped_domain_map(
4647 __isl_take isl_union_set *uset);
4649 The functions above construct a (basic, regular or union) relation
4650 that maps (a wrapped version of) the input relation to its domain or range.
4651 C<isl_set_wrapped_domain_map> maps the input set to the domain
4652 of its wrapped relation.
4656 __isl_give isl_basic_set *isl_basic_set_eliminate(
4657 __isl_take isl_basic_set *bset,
4658 enum isl_dim_type type,
4659 unsigned first, unsigned n);
4660 __isl_give isl_set *isl_set_eliminate(
4661 __isl_take isl_set *set, enum isl_dim_type type,
4662 unsigned first, unsigned n);
4663 __isl_give isl_basic_map *isl_basic_map_eliminate(
4664 __isl_take isl_basic_map *bmap,
4665 enum isl_dim_type type,
4666 unsigned first, unsigned n);
4667 __isl_give isl_map *isl_map_eliminate(
4668 __isl_take isl_map *map, enum isl_dim_type type,
4669 unsigned first, unsigned n);
4671 Eliminate the coefficients for the given dimensions from the constraints,
4672 without removing the dimensions.
4674 =item * Constructing a set from a parameter domain
4676 A zero-dimensional (local) space or (basic) set can be constructed
4677 on a given parameter domain using the following functions.
4679 #include <isl/space.h>
4680 __isl_give isl_space *isl_space_set_from_params(
4681 __isl_take isl_space *space);
4683 #include <isl/local_space.h>
4684 __isl_give isl_local_space *
4685 isl_local_space_set_from_params(
4686 __isl_take isl_local_space *ls);
4688 #include <isl/set.h>
4689 __isl_give isl_basic_set *isl_basic_set_from_params(
4690 __isl_take isl_basic_set *bset);
4691 __isl_give isl_set *isl_set_from_params(
4692 __isl_take isl_set *set);
4694 =item * Constructing a relation from one or two sets
4696 Create a relation with the given set(s) as domain and/or range.
4697 If only the domain or the range is specified, then
4698 the range or domain of the created relation is a zero-dimensional
4699 flat anonymous space.
4701 #include <isl/space.h>
4702 __isl_give isl_space *isl_space_from_domain(
4703 __isl_take isl_space *space);
4704 __isl_give isl_space *isl_space_from_range(
4705 __isl_take isl_space *space);
4706 __isl_give isl_space *isl_space_map_from_set(
4707 __isl_take isl_space *space);
4708 __isl_give isl_space *isl_space_map_from_domain_and_range(
4709 __isl_take isl_space *domain,
4710 __isl_take isl_space *range);
4712 #include <isl/local_space.h>
4713 __isl_give isl_local_space *isl_local_space_from_domain(
4714 __isl_take isl_local_space *ls);
4716 #include <isl/map.h>
4717 __isl_give isl_map *isl_map_from_domain(
4718 __isl_take isl_set *set);
4719 __isl_give isl_map *isl_map_from_range(
4720 __isl_take isl_set *set);
4722 #include <isl/union_map.h>
4723 __isl_give isl_union_map *isl_union_map_from_domain(
4724 __isl_take isl_union_set *uset);
4725 __isl_give isl_union_map *isl_union_map_from_range(
4726 __isl_take isl_union_set *uset);
4727 __isl_give isl_union_map *
4728 isl_union_map_from_domain_and_range(
4729 __isl_take isl_union_set *domain,
4730 __isl_take isl_union_set *range);
4732 #include <isl/val.h>
4733 __isl_give isl_multi_val *isl_multi_val_from_range(
4734 __isl_take isl_multi_val *mv);
4736 #include <isl/aff.h>
4737 __isl_give isl_aff *isl_aff_from_range(
4738 __isl_take isl_aff *aff);
4739 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4740 __isl_take isl_multi_aff *ma);
4741 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4742 __isl_take isl_pw_aff *pwa);
4743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4744 __isl_take isl_multi_pw_aff *mpa);
4745 __isl_give isl_multi_union_pw_aff *
4746 isl_multi_union_pw_aff_from_range(
4747 __isl_take isl_multi_union_pw_aff *mupa);
4748 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4749 __isl_take isl_set *set);
4750 __isl_give isl_union_pw_multi_aff *
4751 isl_union_pw_multi_aff_from_domain(
4752 __isl_take isl_union_set *uset);
4754 #include <isl/polynomial.h>
4755 __isl_give isl_pw_qpolynomial *
4756 isl_pw_qpolynomial_from_range(
4757 __isl_take isl_pw_qpolynomial *pwqp);
4758 __isl_give isl_pw_qpolynomial_fold *
4759 isl_pw_qpolynomial_fold_from_range(
4760 __isl_take isl_pw_qpolynomial_fold *pwf);
4764 #include <isl/set.h>
4765 __isl_give isl_basic_set *isl_basic_set_fix_si(
4766 __isl_take isl_basic_set *bset,
4767 enum isl_dim_type type, unsigned pos, int value);
4768 __isl_give isl_basic_set *isl_basic_set_fix_val(
4769 __isl_take isl_basic_set *bset,
4770 enum isl_dim_type type, unsigned pos,
4771 __isl_take isl_val *v);
4772 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4773 enum isl_dim_type type, unsigned pos, int value);
4774 __isl_give isl_set *isl_set_fix_val(
4775 __isl_take isl_set *set,
4776 enum isl_dim_type type, unsigned pos,
4777 __isl_take isl_val *v);
4779 #include <isl/map.h>
4780 __isl_give isl_basic_map *isl_basic_map_fix_si(
4781 __isl_take isl_basic_map *bmap,
4782 enum isl_dim_type type, unsigned pos, int value);
4783 __isl_give isl_basic_map *isl_basic_map_fix_val(
4784 __isl_take isl_basic_map *bmap,
4785 enum isl_dim_type type, unsigned pos,
4786 __isl_take isl_val *v);
4787 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4788 enum isl_dim_type type, unsigned pos, int value);
4789 __isl_give isl_map *isl_map_fix_val(
4790 __isl_take isl_map *map,
4791 enum isl_dim_type type, unsigned pos,
4792 __isl_take isl_val *v);
4794 #include <isl/aff.h>
4795 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4796 __isl_take isl_pw_multi_aff *pma,
4797 enum isl_dim_type type, unsigned pos, int value);
4799 #include <isl/polynomial.h>
4800 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4801 __isl_take isl_pw_qpolynomial *pwqp,
4802 enum isl_dim_type type, unsigned n,
4803 __isl_take isl_val *v);
4804 __isl_give isl_pw_qpolynomial_fold *
4805 isl_pw_qpolynomial_fold_fix_val(
4806 __isl_take isl_pw_qpolynomial_fold *pwf,
4807 enum isl_dim_type type, unsigned n,
4808 __isl_take isl_val *v);
4810 Intersect the set, relation or function domain
4811 with the hyperplane where the given
4812 dimension has the fixed given value.
4814 #include <isl/set.h>
4815 __isl_give isl_basic_set *
4816 isl_basic_set_lower_bound_val(
4817 __isl_take isl_basic_set *bset,
4818 enum isl_dim_type type, unsigned pos,
4819 __isl_take isl_val *value);
4820 __isl_give isl_basic_set *
4821 isl_basic_set_upper_bound_val(
4822 __isl_take isl_basic_set *bset,
4823 enum isl_dim_type type, unsigned pos,
4824 __isl_take isl_val *value);
4825 __isl_give isl_set *isl_set_lower_bound_si(
4826 __isl_take isl_set *set,
4827 enum isl_dim_type type, unsigned pos, int value);
4828 __isl_give isl_set *isl_set_lower_bound_val(
4829 __isl_take isl_set *set,
4830 enum isl_dim_type type, unsigned pos,
4831 __isl_take isl_val *value);
4832 __isl_give isl_set *isl_set_upper_bound_si(
4833 __isl_take isl_set *set,
4834 enum isl_dim_type type, unsigned pos, int value);
4835 __isl_give isl_set *isl_set_upper_bound_val(
4836 __isl_take isl_set *set,
4837 enum isl_dim_type type, unsigned pos,
4838 __isl_take isl_val *value);
4840 #include <isl/map.h>
4841 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4842 __isl_take isl_basic_map *bmap,
4843 enum isl_dim_type type, unsigned pos, int value);
4844 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4845 __isl_take isl_basic_map *bmap,
4846 enum isl_dim_type type, unsigned pos, int value);
4847 __isl_give isl_map *isl_map_lower_bound_si(
4848 __isl_take isl_map *map,
4849 enum isl_dim_type type, unsigned pos, int value);
4850 __isl_give isl_map *isl_map_upper_bound_si(
4851 __isl_take isl_map *map,
4852 enum isl_dim_type type, unsigned pos, int value);
4854 Intersect the set or relation with the half-space where the given
4855 dimension has a value bounded by the fixed given integer value.
4857 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4858 enum isl_dim_type type1, int pos1,
4859 enum isl_dim_type type2, int pos2);
4860 __isl_give isl_basic_map *isl_basic_map_equate(
4861 __isl_take isl_basic_map *bmap,
4862 enum isl_dim_type type1, int pos1,
4863 enum isl_dim_type type2, int pos2);
4864 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4865 enum isl_dim_type type1, int pos1,
4866 enum isl_dim_type type2, int pos2);
4868 Intersect the set or relation with the hyperplane where the given
4869 dimensions are equal to each other.
4871 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4872 enum isl_dim_type type1, int pos1,
4873 enum isl_dim_type type2, int pos2);
4875 Intersect the relation with the hyperplane where the given
4876 dimensions have opposite values.
4878 __isl_give isl_map *isl_map_order_le(
4879 __isl_take isl_map *map,
4880 enum isl_dim_type type1, int pos1,
4881 enum isl_dim_type type2, int pos2);
4882 __isl_give isl_basic_map *isl_basic_map_order_ge(
4883 __isl_take isl_basic_map *bmap,
4884 enum isl_dim_type type1, int pos1,
4885 enum isl_dim_type type2, int pos2);
4886 __isl_give isl_map *isl_map_order_ge(
4887 __isl_take isl_map *map,
4888 enum isl_dim_type type1, int pos1,
4889 enum isl_dim_type type2, int pos2);
4890 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4891 enum isl_dim_type type1, int pos1,
4892 enum isl_dim_type type2, int pos2);
4893 __isl_give isl_basic_map *isl_basic_map_order_gt(
4894 __isl_take isl_basic_map *bmap,
4895 enum isl_dim_type type1, int pos1,
4896 enum isl_dim_type type2, int pos2);
4897 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4898 enum isl_dim_type type1, int pos1,
4899 enum isl_dim_type type2, int pos2);
4901 Intersect the relation with the half-space where the given
4902 dimensions satisfy the given ordering.
4904 #include <isl/union_set.h>
4905 __isl_give isl_union_map *isl_union_map_remove_map_if(
4906 __isl_take isl_union_map *umap,
4907 isl_bool (*fn)(__isl_keep isl_map *map,
4908 void *user), void *user);
4910 This function calls the callback function once for each
4911 pair of spaces for which there are elements in the input.
4912 If the callback returns C<isl_bool_true>, then all those elements
4913 are removed from the result. The only remaining elements in the output
4914 are then those for which the callback returns C<isl_bool_false>.
4918 #include <isl/aff.h>
4919 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4920 __isl_take isl_aff *aff);
4921 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4922 __isl_take isl_aff *aff);
4923 __isl_give isl_set *isl_pw_aff_pos_set(
4924 __isl_take isl_pw_aff *pa);
4925 __isl_give isl_set *isl_pw_aff_nonneg_set(
4926 __isl_take isl_pw_aff *pwaff);
4927 __isl_give isl_set *isl_pw_aff_zero_set(
4928 __isl_take isl_pw_aff *pwaff);
4929 __isl_give isl_set *isl_pw_aff_non_zero_set(
4930 __isl_take isl_pw_aff *pwaff);
4931 __isl_give isl_union_set *
4932 isl_union_pw_aff_zero_union_set(
4933 __isl_take isl_union_pw_aff *upa);
4934 __isl_give isl_union_set *
4935 isl_multi_union_pw_aff_zero_union_set(
4936 __isl_take isl_multi_union_pw_aff *mupa);
4938 The function C<isl_aff_neg_basic_set> returns a basic set
4939 containing those elements in the domain space
4940 of C<aff> where C<aff> is negative.
4941 The function C<isl_pw_aff_nonneg_set> returns a set
4942 containing those elements in the domain
4943 of C<pwaff> where C<pwaff> is non-negative.
4944 The function C<isl_multi_union_pw_aff_zero_union_set>
4945 returns a union set containing those elements
4946 in the domains of its elements where they are all zero.
4950 __isl_give isl_map *isl_set_identity(
4951 __isl_take isl_set *set);
4952 __isl_give isl_union_map *isl_union_set_identity(
4953 __isl_take isl_union_set *uset);
4954 __isl_give isl_union_pw_multi_aff *
4955 isl_union_set_identity_union_pw_multi_aff(
4956 __isl_take isl_union_set *uset);
4958 Construct an identity relation on the given (union) set.
4960 =item * Function Extraction
4962 A piecewise quasi affine expression that is equal to 1 on a set
4963 and 0 outside the set can be created using the following function.
4965 #include <isl/aff.h>
4966 __isl_give isl_pw_aff *isl_set_indicator_function(
4967 __isl_take isl_set *set);
4969 A piecewise multiple quasi affine expression can be extracted
4970 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4971 and the C<isl_map> is single-valued.
4972 In case of a conversion from an C<isl_union_map>
4973 to an C<isl_union_pw_multi_aff>, these properties need to hold
4974 in each domain space.
4975 A conversion to a C<isl_multi_union_pw_aff> additionally
4976 requires that the input is non-empty and involves only a single
4979 #include <isl/aff.h>
4980 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4981 __isl_take isl_set *set);
4982 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4983 __isl_take isl_map *map);
4985 __isl_give isl_union_pw_multi_aff *
4986 isl_union_pw_multi_aff_from_union_set(
4987 __isl_take isl_union_set *uset);
4988 __isl_give isl_union_pw_multi_aff *
4989 isl_union_pw_multi_aff_from_union_map(
4990 __isl_take isl_union_map *umap);
4992 __isl_give isl_multi_union_pw_aff *
4993 isl_multi_union_pw_aff_from_union_map(
4994 __isl_take isl_union_map *umap);
4998 __isl_give isl_basic_set *isl_basic_map_deltas(
4999 __isl_take isl_basic_map *bmap);
5000 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5001 __isl_give isl_union_set *isl_union_map_deltas(
5002 __isl_take isl_union_map *umap);
5004 These functions return a (basic) set containing the differences
5005 between image elements and corresponding domain elements in the input.
5007 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5008 __isl_take isl_basic_map *bmap);
5009 __isl_give isl_map *isl_map_deltas_map(
5010 __isl_take isl_map *map);
5011 __isl_give isl_union_map *isl_union_map_deltas_map(
5012 __isl_take isl_union_map *umap);
5014 The functions above construct a (basic, regular or union) relation
5015 that maps (a wrapped version of) the input relation to its delta set.
5019 Simplify the representation of a set, relation or functions by trying
5020 to combine pairs of basic sets or relations into a single
5021 basic set or relation.
5023 #include <isl/set.h>
5024 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5026 #include <isl/map.h>
5027 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5029 #include <isl/union_set.h>
5030 __isl_give isl_union_set *isl_union_set_coalesce(
5031 __isl_take isl_union_set *uset);
5033 #include <isl/union_map.h>
5034 __isl_give isl_union_map *isl_union_map_coalesce(
5035 __isl_take isl_union_map *umap);
5037 #include <isl/aff.h>
5038 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5039 __isl_take isl_pw_aff *pwqp);
5040 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5041 __isl_take isl_pw_multi_aff *pma);
5042 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5043 __isl_take isl_multi_pw_aff *mpa);
5044 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5045 __isl_take isl_union_pw_aff *upa);
5046 __isl_give isl_union_pw_multi_aff *
5047 isl_union_pw_multi_aff_coalesce(
5048 __isl_take isl_union_pw_multi_aff *upma);
5049 __isl_give isl_multi_union_pw_aff *
5050 isl_multi_union_pw_aff_coalesce(
5051 __isl_take isl_multi_union_pw_aff *aff);
5053 #include <isl/polynomial.h>
5054 __isl_give isl_pw_qpolynomial_fold *
5055 isl_pw_qpolynomial_fold_coalesce(
5056 __isl_take isl_pw_qpolynomial_fold *pwf);
5057 __isl_give isl_union_pw_qpolynomial *
5058 isl_union_pw_qpolynomial_coalesce(
5059 __isl_take isl_union_pw_qpolynomial *upwqp);
5060 __isl_give isl_union_pw_qpolynomial_fold *
5061 isl_union_pw_qpolynomial_fold_coalesce(
5062 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5064 One of the methods for combining pairs of basic sets or relations
5065 can result in coefficients that are much larger than those that appear
5066 in the constraints of the input. By default, the coefficients are
5067 not allowed to grow larger, but this can be changed by unsetting
5068 the following option.
5070 isl_stat isl_options_set_coalesce_bounded_wrapping(
5071 isl_ctx *ctx, int val);
5072 int isl_options_get_coalesce_bounded_wrapping(
5075 =item * Detecting equalities
5077 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5078 __isl_take isl_basic_set *bset);
5079 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5080 __isl_take isl_basic_map *bmap);
5081 __isl_give isl_set *isl_set_detect_equalities(
5082 __isl_take isl_set *set);
5083 __isl_give isl_map *isl_map_detect_equalities(
5084 __isl_take isl_map *map);
5085 __isl_give isl_union_set *isl_union_set_detect_equalities(
5086 __isl_take isl_union_set *uset);
5087 __isl_give isl_union_map *isl_union_map_detect_equalities(
5088 __isl_take isl_union_map *umap);
5090 Simplify the representation of a set or relation by detecting implicit
5093 =item * Removing redundant constraints
5095 #include <isl/set.h>
5096 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5097 __isl_take isl_basic_set *bset);
5098 __isl_give isl_set *isl_set_remove_redundancies(
5099 __isl_take isl_set *set);
5101 #include <isl/union_set.h>
5102 __isl_give isl_union_set *
5103 isl_union_set_remove_redundancies(
5104 __isl_take isl_union_set *uset);
5106 #include <isl/map.h>
5107 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5108 __isl_take isl_basic_map *bmap);
5109 __isl_give isl_map *isl_map_remove_redundancies(
5110 __isl_take isl_map *map);
5112 #include <isl/union_map.h>
5113 __isl_give isl_union_map *
5114 isl_union_map_remove_redundancies(
5115 __isl_take isl_union_map *umap);
5119 __isl_give isl_basic_set *isl_set_convex_hull(
5120 __isl_take isl_set *set);
5121 __isl_give isl_basic_map *isl_map_convex_hull(
5122 __isl_take isl_map *map);
5124 If the input set or relation has any existentially quantified
5125 variables, then the result of these operations is currently undefined.
5129 #include <isl/set.h>
5130 __isl_give isl_basic_set *
5131 isl_set_unshifted_simple_hull(
5132 __isl_take isl_set *set);
5133 __isl_give isl_basic_set *isl_set_simple_hull(
5134 __isl_take isl_set *set);
5135 __isl_give isl_basic_set *
5136 isl_set_plain_unshifted_simple_hull(
5137 __isl_take isl_set *set);
5138 __isl_give isl_basic_set *
5139 isl_set_unshifted_simple_hull_from_set_list(
5140 __isl_take isl_set *set,
5141 __isl_take isl_set_list *list);
5143 #include <isl/map.h>
5144 __isl_give isl_basic_map *
5145 isl_map_unshifted_simple_hull(
5146 __isl_take isl_map *map);
5147 __isl_give isl_basic_map *isl_map_simple_hull(
5148 __isl_take isl_map *map);
5149 __isl_give isl_basic_map *
5150 isl_map_plain_unshifted_simple_hull(
5151 __isl_take isl_map *map);
5152 __isl_give isl_basic_map *
5153 isl_map_unshifted_simple_hull_from_map_list(
5154 __isl_take isl_map *map,
5155 __isl_take isl_map_list *list);
5157 #include <isl/union_map.h>
5158 __isl_give isl_union_map *isl_union_map_simple_hull(
5159 __isl_take isl_union_map *umap);
5161 These functions compute a single basic set or relation
5162 that contains the whole input set or relation.
5163 In particular, the output is described by translates
5164 of the constraints describing the basic sets or relations in the input.
5165 In case of C<isl_set_unshifted_simple_hull>, only the original
5166 constraints are used, without any translation.
5167 In case of C<isl_set_plain_unshifted_simple_hull> and
5168 C<isl_map_plain_unshifted_simple_hull>, the result is described
5169 by original constraints that are obviously satisfied
5170 by the entire input set or relation.
5171 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5172 C<isl_map_unshifted_simple_hull_from_map_list>, the
5173 constraints are taken from the elements of the second argument.
5177 (See \autoref{s:simple hull}.)
5183 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5184 __isl_take isl_basic_set *bset);
5185 __isl_give isl_basic_set *isl_set_affine_hull(
5186 __isl_take isl_set *set);
5187 __isl_give isl_union_set *isl_union_set_affine_hull(
5188 __isl_take isl_union_set *uset);
5189 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5190 __isl_take isl_basic_map *bmap);
5191 __isl_give isl_basic_map *isl_map_affine_hull(
5192 __isl_take isl_map *map);
5193 __isl_give isl_union_map *isl_union_map_affine_hull(
5194 __isl_take isl_union_map *umap);
5196 In case of union sets and relations, the affine hull is computed
5199 =item * Polyhedral hull
5201 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5202 __isl_take isl_set *set);
5203 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5204 __isl_take isl_map *map);
5205 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5206 __isl_take isl_union_set *uset);
5207 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5208 __isl_take isl_union_map *umap);
5210 These functions compute a single basic set or relation
5211 not involving any existentially quantified variables
5212 that contains the whole input set or relation.
5213 In case of union sets and relations, the polyhedral hull is computed
5216 =item * Other approximations
5218 #include <isl/set.h>
5219 __isl_give isl_basic_set *
5220 isl_basic_set_drop_constraints_involving_dims(
5221 __isl_take isl_basic_set *bset,
5222 enum isl_dim_type type,
5223 unsigned first, unsigned n);
5224 __isl_give isl_basic_set *
5225 isl_basic_set_drop_constraints_not_involving_dims(
5226 __isl_take isl_basic_set *bset,
5227 enum isl_dim_type type,
5228 unsigned first, unsigned n);
5229 __isl_give isl_set *
5230 isl_set_drop_constraints_involving_dims(
5231 __isl_take isl_set *set,
5232 enum isl_dim_type type,
5233 unsigned first, unsigned n);
5234 __isl_give isl_set *
5235 isl_set_drop_constraints_not_involving_dims(
5236 __isl_take isl_set *set,
5237 enum isl_dim_type type,
5238 unsigned first, unsigned n);
5240 #include <isl/map.h>
5241 __isl_give isl_basic_map *
5242 isl_basic_map_drop_constraints_involving_dims(
5243 __isl_take isl_basic_map *bmap,
5244 enum isl_dim_type type,
5245 unsigned first, unsigned n);
5246 __isl_give isl_basic_map *
5247 isl_basic_map_drop_constraints_not_involving_dims(
5248 __isl_take isl_basic_map *bmap,
5249 enum isl_dim_type type,
5250 unsigned first, unsigned n);
5251 __isl_give isl_map *
5252 isl_map_drop_constraints_involving_dims(
5253 __isl_take isl_map *map,
5254 enum isl_dim_type type,
5255 unsigned first, unsigned n);
5256 __isl_give isl_map *
5257 isl_map_drop_constraints_not_involving_dims(
5258 __isl_take isl_map *map,
5259 enum isl_dim_type type,
5260 unsigned first, unsigned n);
5262 These functions drop any constraints (not) involving the specified dimensions.
5263 Note that the result depends on the representation of the input.
5265 #include <isl/polynomial.h>
5266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5267 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5268 __isl_give isl_union_pw_qpolynomial *
5269 isl_union_pw_qpolynomial_to_polynomial(
5270 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5272 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5273 the polynomial will be an overapproximation. If C<sign> is negative,
5274 it will be an underapproximation. If C<sign> is zero, the approximation
5275 will lie somewhere in between.
5279 __isl_give isl_basic_set *isl_basic_set_sample(
5280 __isl_take isl_basic_set *bset);
5281 __isl_give isl_basic_set *isl_set_sample(
5282 __isl_take isl_set *set);
5283 __isl_give isl_basic_map *isl_basic_map_sample(
5284 __isl_take isl_basic_map *bmap);
5285 __isl_give isl_basic_map *isl_map_sample(
5286 __isl_take isl_map *map);
5288 If the input (basic) set or relation is non-empty, then return
5289 a singleton subset of the input. Otherwise, return an empty set.
5291 =item * Optimization
5293 #include <isl/ilp.h>
5294 __isl_give isl_val *isl_basic_set_max_val(
5295 __isl_keep isl_basic_set *bset,
5296 __isl_keep isl_aff *obj);
5297 __isl_give isl_val *isl_set_min_val(
5298 __isl_keep isl_set *set,
5299 __isl_keep isl_aff *obj);
5300 __isl_give isl_val *isl_set_max_val(
5301 __isl_keep isl_set *set,
5302 __isl_keep isl_aff *obj);
5303 __isl_give isl_multi_val *
5304 isl_union_set_min_multi_union_pw_aff(
5305 __isl_keep isl_union_set *set,
5306 __isl_keep isl_multi_union_pw_aff *obj);
5308 Compute the minimum or maximum of the integer affine expression C<obj>
5309 over the points in C<set>, returning the result in C<opt>.
5310 The result is C<NULL> in case of an error, the optimal value in case
5311 there is one, negative infinity or infinity if the problem is unbounded and
5312 NaN if the problem is empty.
5314 #include <isl/ilp.h>
5315 __isl_give isl_val *isl_basic_set_dim_max_val(
5316 __isl_take isl_basic_set *bset, int pos);
5318 Return the maximal value attained by the given set dimension,
5319 independently of the parameter values and of any other dimensions.
5320 The result is C<NULL> in case of an error, the optimal value in case
5321 there is one, infinity if the problem is unbounded and
5322 NaN if the input is empty.
5324 =item * Parametric optimization
5326 __isl_give isl_pw_aff *isl_set_dim_min(
5327 __isl_take isl_set *set, int pos);
5328 __isl_give isl_pw_aff *isl_set_dim_max(
5329 __isl_take isl_set *set, int pos);
5330 __isl_give isl_pw_aff *isl_map_dim_min(
5331 __isl_take isl_map *map, int pos);
5332 __isl_give isl_pw_aff *isl_map_dim_max(
5333 __isl_take isl_map *map, int pos);
5335 Compute the minimum or maximum of the given set or output dimension
5336 as a function of the parameters (and input dimensions), but independently
5337 of the other set or output dimensions.
5338 For lexicographic optimization, see L<"Lexicographic Optimization">.
5342 The following functions compute either the set of (rational) coefficient
5343 values of valid constraints for the given set or the set of (rational)
5344 values satisfying the constraints with coefficients from the given set.
5345 Internally, these two sets of functions perform essentially the
5346 same operations, except that the set of coefficients is assumed to
5347 be a cone, while the set of values may be any polyhedron.
5348 The current implementation is based on the Farkas lemma and
5349 Fourier-Motzkin elimination, but this may change or be made optional
5350 in future. In particular, future implementations may use different
5351 dualization algorithms or skip the elimination step.
5353 #include <isl/set.h>
5354 __isl_give isl_basic_set *isl_basic_set_coefficients(
5355 __isl_take isl_basic_set *bset);
5356 __isl_give isl_basic_set_list *
5357 isl_basic_set_list_coefficients(
5358 __isl_take isl_basic_set_list *list);
5359 __isl_give isl_basic_set *isl_set_coefficients(
5360 __isl_take isl_set *set);
5361 __isl_give isl_union_set *isl_union_set_coefficients(
5362 __isl_take isl_union_set *bset);
5363 __isl_give isl_basic_set *isl_basic_set_solutions(
5364 __isl_take isl_basic_set *bset);
5365 __isl_give isl_basic_set *isl_set_solutions(
5366 __isl_take isl_set *set);
5367 __isl_give isl_union_set *isl_union_set_solutions(
5368 __isl_take isl_union_set *bset);
5372 __isl_give isl_map *isl_map_fixed_power_val(
5373 __isl_take isl_map *map,
5374 __isl_take isl_val *exp);
5375 __isl_give isl_union_map *
5376 isl_union_map_fixed_power_val(
5377 __isl_take isl_union_map *umap,
5378 __isl_take isl_val *exp);
5380 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5381 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5382 of C<map> is computed.
5384 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5386 __isl_give isl_union_map *isl_union_map_power(
5387 __isl_take isl_union_map *umap, int *exact);
5389 Compute a parametric representation for all positive powers I<k> of C<map>.
5390 The result maps I<k> to a nested relation corresponding to the
5391 I<k>th power of C<map>.
5392 The result may be an overapproximation. If the result is known to be exact,
5393 then C<*exact> is set to C<1>.
5395 =item * Transitive closure
5397 __isl_give isl_map *isl_map_transitive_closure(
5398 __isl_take isl_map *map, int *exact);
5399 __isl_give isl_union_map *isl_union_map_transitive_closure(
5400 __isl_take isl_union_map *umap, int *exact);
5402 Compute the transitive closure of C<map>.
5403 The result may be an overapproximation. If the result is known to be exact,
5404 then C<*exact> is set to C<1>.
5406 =item * Reaching path lengths
5408 __isl_give isl_map *isl_map_reaching_path_lengths(
5409 __isl_take isl_map *map, int *exact);
5411 Compute a relation that maps each element in the range of C<map>
5412 to the lengths of all paths composed of edges in C<map> that
5413 end up in the given element.
5414 The result may be an overapproximation. If the result is known to be exact,
5415 then C<*exact> is set to C<1>.
5416 To compute the I<maximal> path length, the resulting relation
5417 should be postprocessed by C<isl_map_lexmax>.
5418 In particular, if the input relation is a dependence relation
5419 (mapping sources to sinks), then the maximal path length corresponds
5420 to the free schedule.
5421 Note, however, that C<isl_map_lexmax> expects the maximum to be
5422 finite, so if the path lengths are unbounded (possibly due to
5423 the overapproximation), then you will get an error message.
5427 #include <isl/space.h>
5428 __isl_give isl_space *isl_space_wrap(
5429 __isl_take isl_space *space);
5430 __isl_give isl_space *isl_space_unwrap(
5431 __isl_take isl_space *space);
5433 #include <isl/local_space.h>
5434 __isl_give isl_local_space *isl_local_space_wrap(
5435 __isl_take isl_local_space *ls);
5437 #include <isl/set.h>
5438 __isl_give isl_basic_map *isl_basic_set_unwrap(
5439 __isl_take isl_basic_set *bset);
5440 __isl_give isl_map *isl_set_unwrap(
5441 __isl_take isl_set *set);
5443 #include <isl/map.h>
5444 __isl_give isl_basic_set *isl_basic_map_wrap(
5445 __isl_take isl_basic_map *bmap);
5446 __isl_give isl_set *isl_map_wrap(
5447 __isl_take isl_map *map);
5449 #include <isl/union_set.h>
5450 __isl_give isl_union_map *isl_union_set_unwrap(
5451 __isl_take isl_union_set *uset);
5453 #include <isl/union_map.h>
5454 __isl_give isl_union_set *isl_union_map_wrap(
5455 __isl_take isl_union_map *umap);
5457 The input to C<isl_space_unwrap> should
5458 be the space of a set, while that of
5459 C<isl_space_wrap> should be the space of a relation.
5460 Conversely, the output of C<isl_space_unwrap> is the space
5461 of a relation, while that of C<isl_space_wrap> is the space of a set.
5465 Remove any internal structure of domain (and range) of the given
5466 set or relation. If there is any such internal structure in the input,
5467 then the name of the space is also removed.
5469 #include <isl/space.h>
5470 __isl_give isl_space *isl_space_flatten_domain(
5471 __isl_take isl_space *space);
5472 __isl_give isl_space *isl_space_flatten_range(
5473 __isl_take isl_space *space);
5475 #include <isl/local_space.h>
5476 __isl_give isl_local_space *
5477 isl_local_space_flatten_domain(
5478 __isl_take isl_local_space *ls);
5479 __isl_give isl_local_space *
5480 isl_local_space_flatten_range(
5481 __isl_take isl_local_space *ls);
5483 #include <isl/set.h>
5484 __isl_give isl_basic_set *isl_basic_set_flatten(
5485 __isl_take isl_basic_set *bset);
5486 __isl_give isl_set *isl_set_flatten(
5487 __isl_take isl_set *set);
5489 #include <isl/map.h>
5490 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5491 __isl_take isl_basic_map *bmap);
5492 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5493 __isl_take isl_basic_map *bmap);
5494 __isl_give isl_map *isl_map_flatten_range(
5495 __isl_take isl_map *map);
5496 __isl_give isl_map *isl_map_flatten_domain(
5497 __isl_take isl_map *map);
5498 __isl_give isl_basic_map *isl_basic_map_flatten(
5499 __isl_take isl_basic_map *bmap);
5500 __isl_give isl_map *isl_map_flatten(
5501 __isl_take isl_map *map);
5503 #include <isl/val.h>
5504 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5505 __isl_take isl_multi_val *mv);
5507 #include <isl/aff.h>
5508 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5509 __isl_take isl_multi_aff *ma);
5510 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5511 __isl_take isl_multi_aff *ma);
5512 __isl_give isl_multi_pw_aff *
5513 isl_multi_pw_aff_flatten_range(
5514 __isl_take isl_multi_pw_aff *mpa);
5515 __isl_give isl_multi_union_pw_aff *
5516 isl_multi_union_pw_aff_flatten_range(
5517 __isl_take isl_multi_union_pw_aff *mupa);
5519 #include <isl/map.h>
5520 __isl_give isl_map *isl_set_flatten_map(
5521 __isl_take isl_set *set);
5523 The function above constructs a relation
5524 that maps the input set to a flattened version of the set.
5528 Lift the input set to a space with extra dimensions corresponding
5529 to the existentially quantified variables in the input.
5530 In particular, the result lives in a wrapped map where the domain
5531 is the original space and the range corresponds to the original
5532 existentially quantified variables.
5534 #include <isl/set.h>
5535 __isl_give isl_basic_set *isl_basic_set_lift(
5536 __isl_take isl_basic_set *bset);
5537 __isl_give isl_set *isl_set_lift(
5538 __isl_take isl_set *set);
5539 __isl_give isl_union_set *isl_union_set_lift(
5540 __isl_take isl_union_set *uset);
5542 Given a local space that contains the existentially quantified
5543 variables of a set, a basic relation that, when applied to
5544 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5545 can be constructed using the following function.
5547 #include <isl/local_space.h>
5548 __isl_give isl_basic_map *isl_local_space_lifting(
5549 __isl_take isl_local_space *ls);
5551 #include <isl/aff.h>
5552 __isl_give isl_multi_aff *isl_multi_aff_lift(
5553 __isl_take isl_multi_aff *maff,
5554 __isl_give isl_local_space **ls);
5556 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5557 then it is assigned the local space that lies at the basis of
5558 the lifting applied.
5560 =item * Internal Product
5562 #include <isl/space.h>
5563 __isl_give isl_space *isl_space_zip(
5564 __isl_take isl_space *space);
5566 #include <isl/map.h>
5567 __isl_give isl_basic_map *isl_basic_map_zip(
5568 __isl_take isl_basic_map *bmap);
5569 __isl_give isl_map *isl_map_zip(
5570 __isl_take isl_map *map);
5572 #include <isl/union_map.h>
5573 __isl_give isl_union_map *isl_union_map_zip(
5574 __isl_take isl_union_map *umap);
5576 Given a relation with nested relations for domain and range,
5577 interchange the range of the domain with the domain of the range.
5581 #include <isl/space.h>
5582 __isl_give isl_space *isl_space_curry(
5583 __isl_take isl_space *space);
5584 __isl_give isl_space *isl_space_uncurry(
5585 __isl_take isl_space *space);
5587 #include <isl/map.h>
5588 __isl_give isl_basic_map *isl_basic_map_curry(
5589 __isl_take isl_basic_map *bmap);
5590 __isl_give isl_basic_map *isl_basic_map_uncurry(
5591 __isl_take isl_basic_map *bmap);
5592 __isl_give isl_map *isl_map_curry(
5593 __isl_take isl_map *map);
5594 __isl_give isl_map *isl_map_uncurry(
5595 __isl_take isl_map *map);
5597 #include <isl/union_map.h>
5598 __isl_give isl_union_map *isl_union_map_curry(
5599 __isl_take isl_union_map *umap);
5600 __isl_give isl_union_map *isl_union_map_uncurry(
5601 __isl_take isl_union_map *umap);
5603 Given a relation with a nested relation for domain,
5604 the C<curry> functions
5605 move the range of the nested relation out of the domain
5606 and use it as the domain of a nested relation in the range,
5607 with the original range as range of this nested relation.
5608 The C<uncurry> functions perform the inverse operation.
5610 #include <isl/space.h>
5611 __isl_give isl_space *isl_space_range_curry(
5612 __isl_take isl_space *space);
5614 #include <isl/map.h>
5615 __isl_give isl_map *isl_map_range_curry(
5616 __isl_take isl_map *map);
5618 #include <isl/union_map.h>
5619 __isl_give isl_union_map *isl_union_map_range_curry(
5620 __isl_take isl_union_map *umap);
5622 These functions apply the currying to the relation that
5623 is nested inside the range of the input.
5625 =item * Aligning parameters
5627 Change the order of the parameters of the given set, relation
5629 such that the first parameters match those of C<model>.
5630 This may involve the introduction of extra parameters.
5631 All parameters need to be named.
5633 #include <isl/space.h>
5634 __isl_give isl_space *isl_space_align_params(
5635 __isl_take isl_space *space1,
5636 __isl_take isl_space *space2)
5638 #include <isl/set.h>
5639 __isl_give isl_basic_set *isl_basic_set_align_params(
5640 __isl_take isl_basic_set *bset,
5641 __isl_take isl_space *model);
5642 __isl_give isl_set *isl_set_align_params(
5643 __isl_take isl_set *set,
5644 __isl_take isl_space *model);
5646 #include <isl/map.h>
5647 __isl_give isl_basic_map *isl_basic_map_align_params(
5648 __isl_take isl_basic_map *bmap,
5649 __isl_take isl_space *model);
5650 __isl_give isl_map *isl_map_align_params(
5651 __isl_take isl_map *map,
5652 __isl_take isl_space *model);
5654 #include <isl/val.h>
5655 __isl_give isl_multi_val *isl_multi_val_align_params(
5656 __isl_take isl_multi_val *mv,
5657 __isl_take isl_space *model);
5659 #include <isl/aff.h>
5660 __isl_give isl_aff *isl_aff_align_params(
5661 __isl_take isl_aff *aff,
5662 __isl_take isl_space *model);
5663 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5664 __isl_take isl_multi_aff *multi,
5665 __isl_take isl_space *model);
5666 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5667 __isl_take isl_pw_aff *pwaff,
5668 __isl_take isl_space *model);
5669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5670 __isl_take isl_pw_multi_aff *pma,
5671 __isl_take isl_space *model);
5672 __isl_give isl_union_pw_aff *
5673 isl_union_pw_aff_align_params(
5674 __isl_take isl_union_pw_aff *upa,
5675 __isl_take isl_space *model);
5676 __isl_give isl_union_pw_multi_aff *
5677 isl_union_pw_multi_aff_align_params(
5678 __isl_take isl_union_pw_multi_aff *upma,
5679 __isl_take isl_space *model);
5680 __isl_give isl_multi_union_pw_aff *
5681 isl_multi_union_pw_aff_align_params(
5682 __isl_take isl_multi_union_pw_aff *mupa,
5683 __isl_take isl_space *model);
5685 #include <isl/polynomial.h>
5686 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5687 __isl_take isl_qpolynomial *qp,
5688 __isl_take isl_space *model);
5690 =item * Drop unused parameters
5692 Drop parameters that are not referenced by the isl object.
5693 All parameters need to be named.
5695 #include <isl/set.h>
5696 __isl_give isl_basic_set *
5697 isl_basic_set_drop_unused_params(
5698 __isl_take isl_basic_set *bset);
5699 __isl_give isl_set *isl_set_drop_unused_params(
5700 __isl_take isl_set *set);
5702 #include <isl/map.h>
5703 __isl_give isl_basic_map *
5704 isl_basic_map_drop_unused_params(
5705 __isl_take isl_basic_map *bmap);
5706 __isl_give isl_map *isl_map_drop_unused_params(
5707 __isl_take isl_map *map);
5709 #include <isl/aff.h>
5710 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5711 __isl_take isl_pw_aff *pa);
5712 __isl_give isl_pw_multi_aff *
5713 isl_pw_multi_aff_drop_unused_params(
5714 __isl_take isl_pw_multi_aff *pma);
5716 #include <isl/polynomial.h>
5717 __isl_give isl_pw_qpolynomial *
5718 isl_pw_qpolynomial_drop_unused_params(
5719 __isl_take isl_pw_qpolynomial *pwqp);
5720 __isl_give isl_pw_qpolynomial_fold *
5721 isl_pw_qpolynomial_fold_drop_unused_params(
5722 __isl_take isl_pw_qpolynomial_fold *pwf);
5724 =item * Unary Arithmetic Operations
5726 #include <isl/set.h>
5727 __isl_give isl_set *isl_set_neg(
5728 __isl_take isl_set *set);
5729 #include <isl/map.h>
5730 __isl_give isl_map *isl_map_neg(
5731 __isl_take isl_map *map);
5733 C<isl_set_neg> constructs a set containing the opposites of
5734 the elements in its argument.
5735 The domain of the result of C<isl_map_neg> is the same
5736 as the domain of its argument. The corresponding range
5737 elements are the opposites of the corresponding range
5738 elements in the argument.
5740 #include <isl/val.h>
5741 __isl_give isl_multi_val *isl_multi_val_neg(
5742 __isl_take isl_multi_val *mv);
5744 #include <isl/aff.h>
5745 __isl_give isl_aff *isl_aff_neg(
5746 __isl_take isl_aff *aff);
5747 __isl_give isl_multi_aff *isl_multi_aff_neg(
5748 __isl_take isl_multi_aff *ma);
5749 __isl_give isl_pw_aff *isl_pw_aff_neg(
5750 __isl_take isl_pw_aff *pwaff);
5751 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5752 __isl_take isl_pw_multi_aff *pma);
5753 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5754 __isl_take isl_multi_pw_aff *mpa);
5755 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5756 __isl_take isl_union_pw_aff *upa);
5757 __isl_give isl_union_pw_multi_aff *
5758 isl_union_pw_multi_aff_neg(
5759 __isl_take isl_union_pw_multi_aff *upma);
5760 __isl_give isl_multi_union_pw_aff *
5761 isl_multi_union_pw_aff_neg(
5762 __isl_take isl_multi_union_pw_aff *mupa);
5763 __isl_give isl_aff *isl_aff_ceil(
5764 __isl_take isl_aff *aff);
5765 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5766 __isl_take isl_pw_aff *pwaff);
5767 __isl_give isl_aff *isl_aff_floor(
5768 __isl_take isl_aff *aff);
5769 __isl_give isl_multi_aff *isl_multi_aff_floor(
5770 __isl_take isl_multi_aff *ma);
5771 __isl_give isl_pw_aff *isl_pw_aff_floor(
5772 __isl_take isl_pw_aff *pwaff);
5773 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5774 __isl_take isl_union_pw_aff *upa);
5775 __isl_give isl_multi_union_pw_aff *
5776 isl_multi_union_pw_aff_floor(
5777 __isl_take isl_multi_union_pw_aff *mupa);
5779 #include <isl/aff.h>
5780 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5781 __isl_take isl_pw_aff_list *list);
5782 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5783 __isl_take isl_pw_aff_list *list);
5785 #include <isl/polynomial.h>
5786 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5787 __isl_take isl_qpolynomial *qp);
5788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5789 __isl_take isl_pw_qpolynomial *pwqp);
5790 __isl_give isl_union_pw_qpolynomial *
5791 isl_union_pw_qpolynomial_neg(
5792 __isl_take isl_union_pw_qpolynomial *upwqp);
5793 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5794 __isl_take isl_qpolynomial *qp,
5796 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5797 __isl_take isl_pw_qpolynomial *pwqp,
5802 The following functions evaluate a function in a point.
5804 #include <isl/aff.h>
5805 __isl_give isl_val *isl_aff_eval(
5806 __isl_take isl_aff *aff,
5807 __isl_take isl_point *pnt);
5808 __isl_give isl_val *isl_pw_aff_eval(
5809 __isl_take isl_pw_aff *pa,
5810 __isl_take isl_point *pnt);
5812 #include <isl/polynomial.h>
5813 __isl_give isl_val *isl_pw_qpolynomial_eval(
5814 __isl_take isl_pw_qpolynomial *pwqp,
5815 __isl_take isl_point *pnt);
5816 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5817 __isl_take isl_pw_qpolynomial_fold *pwf,
5818 __isl_take isl_point *pnt);
5819 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5820 __isl_take isl_union_pw_qpolynomial *upwqp,
5821 __isl_take isl_point *pnt);
5822 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5823 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5824 __isl_take isl_point *pnt);
5826 These functions return NaN when evaluated at a void point.
5827 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5828 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5829 when the function is evaluated outside its explicit domain.
5831 =item * Dimension manipulation
5833 It is usually not advisable to directly change the (input or output)
5834 space of a set or a relation as this removes the name and the internal
5835 structure of the space. However, the functions below can be useful
5836 to add new parameters, assuming
5837 C<isl_set_align_params> and C<isl_map_align_params>
5840 #include <isl/space.h>
5841 __isl_give isl_space *isl_space_add_dims(
5842 __isl_take isl_space *space,
5843 enum isl_dim_type type, unsigned n);
5844 __isl_give isl_space *isl_space_insert_dims(
5845 __isl_take isl_space *space,
5846 enum isl_dim_type type, unsigned pos, unsigned n);
5847 __isl_give isl_space *isl_space_drop_dims(
5848 __isl_take isl_space *space,
5849 enum isl_dim_type type, unsigned first, unsigned n);
5850 __isl_give isl_space *isl_space_move_dims(
5851 __isl_take isl_space *space,
5852 enum isl_dim_type dst_type, unsigned dst_pos,
5853 enum isl_dim_type src_type, unsigned src_pos,
5856 #include <isl/local_space.h>
5857 __isl_give isl_local_space *isl_local_space_add_dims(
5858 __isl_take isl_local_space *ls,
5859 enum isl_dim_type type, unsigned n);
5860 __isl_give isl_local_space *isl_local_space_insert_dims(
5861 __isl_take isl_local_space *ls,
5862 enum isl_dim_type type, unsigned first, unsigned n);
5863 __isl_give isl_local_space *isl_local_space_drop_dims(
5864 __isl_take isl_local_space *ls,
5865 enum isl_dim_type type, unsigned first, unsigned n);
5867 #include <isl/set.h>
5868 __isl_give isl_basic_set *isl_basic_set_add_dims(
5869 __isl_take isl_basic_set *bset,
5870 enum isl_dim_type type, unsigned n);
5871 __isl_give isl_set *isl_set_add_dims(
5872 __isl_take isl_set *set,
5873 enum isl_dim_type type, unsigned n);
5874 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5875 __isl_take isl_basic_set *bset,
5876 enum isl_dim_type type, unsigned pos,
5878 __isl_give isl_set *isl_set_insert_dims(
5879 __isl_take isl_set *set,
5880 enum isl_dim_type type, unsigned pos, unsigned n);
5881 __isl_give isl_basic_set *isl_basic_set_move_dims(
5882 __isl_take isl_basic_set *bset,
5883 enum isl_dim_type dst_type, unsigned dst_pos,
5884 enum isl_dim_type src_type, unsigned src_pos,
5886 __isl_give isl_set *isl_set_move_dims(
5887 __isl_take isl_set *set,
5888 enum isl_dim_type dst_type, unsigned dst_pos,
5889 enum isl_dim_type src_type, unsigned src_pos,
5892 #include <isl/map.h>
5893 __isl_give isl_basic_map *isl_basic_map_add_dims(
5894 __isl_take isl_basic_map *bmap,
5895 enum isl_dim_type type, unsigned n);
5896 __isl_give isl_map *isl_map_add_dims(
5897 __isl_take isl_map *map,
5898 enum isl_dim_type type, unsigned n);
5899 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5900 __isl_take isl_basic_map *bmap,
5901 enum isl_dim_type type, unsigned pos,
5903 __isl_give isl_map *isl_map_insert_dims(
5904 __isl_take isl_map *map,
5905 enum isl_dim_type type, unsigned pos, unsigned n);
5906 __isl_give isl_basic_map *isl_basic_map_move_dims(
5907 __isl_take isl_basic_map *bmap,
5908 enum isl_dim_type dst_type, unsigned dst_pos,
5909 enum isl_dim_type src_type, unsigned src_pos,
5911 __isl_give isl_map *isl_map_move_dims(
5912 __isl_take isl_map *map,
5913 enum isl_dim_type dst_type, unsigned dst_pos,
5914 enum isl_dim_type src_type, unsigned src_pos,
5917 #include <isl/val.h>
5918 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5919 __isl_take isl_multi_val *mv,
5920 enum isl_dim_type type, unsigned first, unsigned n);
5921 __isl_give isl_multi_val *isl_multi_val_add_dims(
5922 __isl_take isl_multi_val *mv,
5923 enum isl_dim_type type, unsigned n);
5924 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5925 __isl_take isl_multi_val *mv,
5926 enum isl_dim_type type, unsigned first, unsigned n);
5928 #include <isl/aff.h>
5929 __isl_give isl_aff *isl_aff_insert_dims(
5930 __isl_take isl_aff *aff,
5931 enum isl_dim_type type, unsigned first, unsigned n);
5932 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5933 __isl_take isl_multi_aff *ma,
5934 enum isl_dim_type type, unsigned first, unsigned n);
5935 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5936 __isl_take isl_pw_aff *pwaff,
5937 enum isl_dim_type type, unsigned first, unsigned n);
5938 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5939 __isl_take isl_multi_pw_aff *mpa,
5940 enum isl_dim_type type, unsigned first, unsigned n);
5941 __isl_give isl_aff *isl_aff_add_dims(
5942 __isl_take isl_aff *aff,
5943 enum isl_dim_type type, unsigned n);
5944 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5945 __isl_take isl_multi_aff *ma,
5946 enum isl_dim_type type, unsigned n);
5947 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5948 __isl_take isl_pw_aff *pwaff,
5949 enum isl_dim_type type, unsigned n);
5950 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5951 __isl_take isl_multi_pw_aff *mpa,
5952 enum isl_dim_type type, unsigned n);
5953 __isl_give isl_aff *isl_aff_drop_dims(
5954 __isl_take isl_aff *aff,
5955 enum isl_dim_type type, unsigned first, unsigned n);
5956 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5957 __isl_take isl_multi_aff *maff,
5958 enum isl_dim_type type, unsigned first, unsigned n);
5959 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5960 __isl_take isl_pw_aff *pwaff,
5961 enum isl_dim_type type, unsigned first, unsigned n);
5962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5963 __isl_take isl_pw_multi_aff *pma,
5964 enum isl_dim_type type, unsigned first, unsigned n);
5965 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5966 __isl_take isl_union_pw_aff *upa,
5967 enum isl_dim_type type, unsigned first, unsigned n);
5968 __isl_give isl_union_pw_multi_aff *
5969 isl_union_pw_multi_aff_drop_dims(
5970 __isl_take isl_union_pw_multi_aff *upma,
5971 enum isl_dim_type type,
5972 unsigned first, unsigned n);
5973 __isl_give isl_multi_union_pw_aff *
5974 isl_multi_union_pw_aff_drop_dims(
5975 __isl_take isl_multi_union_pw_aff *mupa,
5976 enum isl_dim_type type, unsigned first,
5978 __isl_give isl_aff *isl_aff_move_dims(
5979 __isl_take isl_aff *aff,
5980 enum isl_dim_type dst_type, unsigned dst_pos,
5981 enum isl_dim_type src_type, unsigned src_pos,
5983 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5984 __isl_take isl_multi_aff *ma,
5985 enum isl_dim_type dst_type, unsigned dst_pos,
5986 enum isl_dim_type src_type, unsigned src_pos,
5988 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5989 __isl_take isl_pw_aff *pa,
5990 enum isl_dim_type dst_type, unsigned dst_pos,
5991 enum isl_dim_type src_type, unsigned src_pos,
5993 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5994 __isl_take isl_multi_pw_aff *pma,
5995 enum isl_dim_type dst_type, unsigned dst_pos,
5996 enum isl_dim_type src_type, unsigned src_pos,
5999 #include <isl/polynomial.h>
6000 __isl_give isl_union_pw_qpolynomial *
6001 isl_union_pw_qpolynomial_drop_dims(
6002 __isl_take isl_union_pw_qpolynomial *upwqp,
6003 enum isl_dim_type type,
6004 unsigned first, unsigned n);
6005 __isl_give isl_union_pw_qpolynomial_fold *
6006 isl_union_pw_qpolynomial_fold_drop_dims(
6007 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6008 enum isl_dim_type type,
6009 unsigned first, unsigned n);
6011 The operations on union expressions can only manipulate parameters.
6015 =head2 Binary Operations
6017 The two arguments of a binary operation not only need to live
6018 in the same C<isl_ctx>, they currently also need to have
6019 the same (number of) parameters.
6021 =head3 Basic Operations
6025 =item * Intersection
6027 #include <isl/local_space.h>
6028 __isl_give isl_local_space *isl_local_space_intersect(
6029 __isl_take isl_local_space *ls1,
6030 __isl_take isl_local_space *ls2);
6032 #include <isl/set.h>
6033 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6034 __isl_take isl_basic_set *bset1,
6035 __isl_take isl_basic_set *bset2);
6036 __isl_give isl_basic_set *isl_basic_set_intersect(
6037 __isl_take isl_basic_set *bset1,
6038 __isl_take isl_basic_set *bset2);
6039 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6040 __isl_take struct isl_basic_set_list *list);
6041 __isl_give isl_set *isl_set_intersect_params(
6042 __isl_take isl_set *set,
6043 __isl_take isl_set *params);
6044 __isl_give isl_set *isl_set_intersect(
6045 __isl_take isl_set *set1,
6046 __isl_take isl_set *set2);
6048 #include <isl/map.h>
6049 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6050 __isl_take isl_basic_map *bmap,
6051 __isl_take isl_basic_set *bset);
6052 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6053 __isl_take isl_basic_map *bmap,
6054 __isl_take isl_basic_set *bset);
6055 __isl_give isl_basic_map *isl_basic_map_intersect(
6056 __isl_take isl_basic_map *bmap1,
6057 __isl_take isl_basic_map *bmap2);
6058 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6059 __isl_take isl_basic_map_list *list);
6060 __isl_give isl_map *isl_map_intersect_params(
6061 __isl_take isl_map *map,
6062 __isl_take isl_set *params);
6063 __isl_give isl_map *isl_map_intersect_domain(
6064 __isl_take isl_map *map,
6065 __isl_take isl_set *set);
6066 __isl_give isl_map *isl_map_intersect_range(
6067 __isl_take isl_map *map,
6068 __isl_take isl_set *set);
6069 __isl_give isl_map *isl_map_intersect(
6070 __isl_take isl_map *map1,
6071 __isl_take isl_map *map2);
6072 __isl_give isl_map *
6073 isl_map_intersect_domain_factor_range(
6074 __isl_take isl_map *map,
6075 __isl_take isl_map *factor);
6076 __isl_give isl_map *
6077 isl_map_intersect_range_factor_range(
6078 __isl_take isl_map *map,
6079 __isl_take isl_map *factor);
6081 #include <isl/union_set.h>
6082 __isl_give isl_union_set *isl_union_set_intersect_params(
6083 __isl_take isl_union_set *uset,
6084 __isl_take isl_set *set);
6085 __isl_give isl_union_set *isl_union_set_intersect(
6086 __isl_take isl_union_set *uset1,
6087 __isl_take isl_union_set *uset2);
6089 #include <isl/union_map.h>
6090 __isl_give isl_union_map *isl_union_map_intersect_params(
6091 __isl_take isl_union_map *umap,
6092 __isl_take isl_set *set);
6093 __isl_give isl_union_map *isl_union_map_intersect_domain(
6094 __isl_take isl_union_map *umap,
6095 __isl_take isl_union_set *uset);
6096 __isl_give isl_union_map *isl_union_map_intersect_range(
6097 __isl_take isl_union_map *umap,
6098 __isl_take isl_union_set *uset);
6099 __isl_give isl_union_map *isl_union_map_intersect(
6100 __isl_take isl_union_map *umap1,
6101 __isl_take isl_union_map *umap2);
6102 __isl_give isl_union_map *
6103 isl_union_map_intersect_range_factor_range(
6104 __isl_take isl_union_map *umap,
6105 __isl_take isl_union_map *factor);
6107 #include <isl/aff.h>
6108 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6109 __isl_take isl_pw_aff *pa,
6110 __isl_take isl_set *set);
6111 __isl_give isl_multi_pw_aff *
6112 isl_multi_pw_aff_intersect_domain(
6113 __isl_take isl_multi_pw_aff *mpa,
6114 __isl_take isl_set *domain);
6115 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6116 __isl_take isl_pw_multi_aff *pma,
6117 __isl_take isl_set *set);
6118 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6119 __isl_take isl_union_pw_aff *upa,
6120 __isl_take isl_union_set *uset);
6121 __isl_give isl_union_pw_multi_aff *
6122 isl_union_pw_multi_aff_intersect_domain(
6123 __isl_take isl_union_pw_multi_aff *upma,
6124 __isl_take isl_union_set *uset);
6125 __isl_give isl_multi_union_pw_aff *
6126 isl_multi_union_pw_aff_intersect_domain(
6127 __isl_take isl_multi_union_pw_aff *mupa,
6128 __isl_take isl_union_set *uset);
6129 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6130 __isl_take isl_pw_aff *pa,
6131 __isl_take isl_set *set);
6132 __isl_give isl_multi_pw_aff *
6133 isl_multi_pw_aff_intersect_params(
6134 __isl_take isl_multi_pw_aff *mpa,
6135 __isl_take isl_set *set);
6136 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6137 __isl_take isl_pw_multi_aff *pma,
6138 __isl_take isl_set *set);
6139 __isl_give isl_union_pw_aff *
6140 isl_union_pw_aff_intersect_params(
6141 __isl_take isl_union_pw_aff *upa,
6142 __isl_give isl_union_pw_multi_aff *
6143 isl_union_pw_multi_aff_intersect_params(
6144 __isl_take isl_union_pw_multi_aff *upma,
6145 __isl_take isl_set *set);
6146 __isl_give isl_multi_union_pw_aff *
6147 isl_multi_union_pw_aff_intersect_params(
6148 __isl_take isl_multi_union_pw_aff *mupa,
6149 __isl_take isl_set *params);
6150 isl_multi_union_pw_aff_intersect_range(
6151 __isl_take isl_multi_union_pw_aff *mupa,
6152 __isl_take isl_set *set);
6154 #include <isl/polynomial.h>
6155 __isl_give isl_pw_qpolynomial *
6156 isl_pw_qpolynomial_intersect_domain(
6157 __isl_take isl_pw_qpolynomial *pwpq,
6158 __isl_take isl_set *set);
6159 __isl_give isl_union_pw_qpolynomial *
6160 isl_union_pw_qpolynomial_intersect_domain(
6161 __isl_take isl_union_pw_qpolynomial *upwpq,
6162 __isl_take isl_union_set *uset);
6163 __isl_give isl_union_pw_qpolynomial_fold *
6164 isl_union_pw_qpolynomial_fold_intersect_domain(
6165 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6166 __isl_take isl_union_set *uset);
6167 __isl_give isl_pw_qpolynomial *
6168 isl_pw_qpolynomial_intersect_params(
6169 __isl_take isl_pw_qpolynomial *pwpq,
6170 __isl_take isl_set *set);
6171 __isl_give isl_pw_qpolynomial_fold *
6172 isl_pw_qpolynomial_fold_intersect_params(
6173 __isl_take isl_pw_qpolynomial_fold *pwf,
6174 __isl_take isl_set *set);
6175 __isl_give isl_union_pw_qpolynomial *
6176 isl_union_pw_qpolynomial_intersect_params(
6177 __isl_take isl_union_pw_qpolynomial *upwpq,
6178 __isl_take isl_set *set);
6179 __isl_give isl_union_pw_qpolynomial_fold *
6180 isl_union_pw_qpolynomial_fold_intersect_params(
6181 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6182 __isl_take isl_set *set);
6184 The second argument to the C<_params> functions needs to be
6185 a parametric (basic) set. For the other functions, a parametric set
6186 for either argument is only allowed if the other argument is
6187 a parametric set as well.
6188 The list passed to C<isl_basic_set_list_intersect> needs to have
6189 at least one element and all elements need to live in the same space.
6190 The function C<isl_multi_union_pw_aff_intersect_range>
6191 restricts the input function to those shared domain elements
6192 that map to the specified range.
6196 #include <isl/set.h>
6197 __isl_give isl_set *isl_basic_set_union(
6198 __isl_take isl_basic_set *bset1,
6199 __isl_take isl_basic_set *bset2);
6200 __isl_give isl_set *isl_set_union(
6201 __isl_take isl_set *set1,
6202 __isl_take isl_set *set2);
6203 __isl_give isl_set *isl_set_list_union(
6204 __isl_take isl_set_list *list);
6206 #include <isl/map.h>
6207 __isl_give isl_map *isl_basic_map_union(
6208 __isl_take isl_basic_map *bmap1,
6209 __isl_take isl_basic_map *bmap2);
6210 __isl_give isl_map *isl_map_union(
6211 __isl_take isl_map *map1,
6212 __isl_take isl_map *map2);
6214 #include <isl/union_set.h>
6215 __isl_give isl_union_set *isl_union_set_union(
6216 __isl_take isl_union_set *uset1,
6217 __isl_take isl_union_set *uset2);
6218 __isl_give isl_union_set *isl_union_set_list_union(
6219 __isl_take isl_union_set_list *list);
6221 #include <isl/union_map.h>
6222 __isl_give isl_union_map *isl_union_map_union(
6223 __isl_take isl_union_map *umap1,
6224 __isl_take isl_union_map *umap2);
6226 The list passed to C<isl_set_list_union> needs to have
6227 at least one element and all elements need to live in the same space.
6229 =item * Set difference
6231 #include <isl/set.h>
6232 __isl_give isl_set *isl_set_subtract(
6233 __isl_take isl_set *set1,
6234 __isl_take isl_set *set2);
6236 #include <isl/map.h>
6237 __isl_give isl_map *isl_map_subtract(
6238 __isl_take isl_map *map1,
6239 __isl_take isl_map *map2);
6240 __isl_give isl_map *isl_map_subtract_domain(
6241 __isl_take isl_map *map,
6242 __isl_take isl_set *dom);
6243 __isl_give isl_map *isl_map_subtract_range(
6244 __isl_take isl_map *map,
6245 __isl_take isl_set *dom);
6247 #include <isl/union_set.h>
6248 __isl_give isl_union_set *isl_union_set_subtract(
6249 __isl_take isl_union_set *uset1,
6250 __isl_take isl_union_set *uset2);
6252 #include <isl/union_map.h>
6253 __isl_give isl_union_map *isl_union_map_subtract(
6254 __isl_take isl_union_map *umap1,
6255 __isl_take isl_union_map *umap2);
6256 __isl_give isl_union_map *isl_union_map_subtract_domain(
6257 __isl_take isl_union_map *umap,
6258 __isl_take isl_union_set *dom);
6259 __isl_give isl_union_map *isl_union_map_subtract_range(
6260 __isl_take isl_union_map *umap,
6261 __isl_take isl_union_set *dom);
6263 #include <isl/aff.h>
6264 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6265 __isl_take isl_pw_aff *pa,
6266 __isl_take isl_set *set);
6267 __isl_give isl_pw_multi_aff *
6268 isl_pw_multi_aff_subtract_domain(
6269 __isl_take isl_pw_multi_aff *pma,
6270 __isl_take isl_set *set);
6271 __isl_give isl_union_pw_aff *
6272 isl_union_pw_aff_subtract_domain(
6273 __isl_take isl_union_pw_aff *upa,
6274 __isl_take isl_union_set *uset);
6275 __isl_give isl_union_pw_multi_aff *
6276 isl_union_pw_multi_aff_subtract_domain(
6277 __isl_take isl_union_pw_multi_aff *upma,
6278 __isl_take isl_set *set);
6280 #include <isl/polynomial.h>
6281 __isl_give isl_pw_qpolynomial *
6282 isl_pw_qpolynomial_subtract_domain(
6283 __isl_take isl_pw_qpolynomial *pwpq,
6284 __isl_take isl_set *set);
6285 __isl_give isl_pw_qpolynomial_fold *
6286 isl_pw_qpolynomial_fold_subtract_domain(
6287 __isl_take isl_pw_qpolynomial_fold *pwf,
6288 __isl_take isl_set *set);
6289 __isl_give isl_union_pw_qpolynomial *
6290 isl_union_pw_qpolynomial_subtract_domain(
6291 __isl_take isl_union_pw_qpolynomial *upwpq,
6292 __isl_take isl_union_set *uset);
6293 __isl_give isl_union_pw_qpolynomial_fold *
6294 isl_union_pw_qpolynomial_fold_subtract_domain(
6295 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6296 __isl_take isl_union_set *uset);
6300 #include <isl/space.h>
6301 __isl_give isl_space *isl_space_join(
6302 __isl_take isl_space *left,
6303 __isl_take isl_space *right);
6305 #include <isl/map.h>
6306 __isl_give isl_basic_set *isl_basic_set_apply(
6307 __isl_take isl_basic_set *bset,
6308 __isl_take isl_basic_map *bmap);
6309 __isl_give isl_set *isl_set_apply(
6310 __isl_take isl_set *set,
6311 __isl_take isl_map *map);
6312 __isl_give isl_union_set *isl_union_set_apply(
6313 __isl_take isl_union_set *uset,
6314 __isl_take isl_union_map *umap);
6315 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6316 __isl_take isl_basic_map *bmap1,
6317 __isl_take isl_basic_map *bmap2);
6318 __isl_give isl_basic_map *isl_basic_map_apply_range(
6319 __isl_take isl_basic_map *bmap1,
6320 __isl_take isl_basic_map *bmap2);
6321 __isl_give isl_map *isl_map_apply_domain(
6322 __isl_take isl_map *map1,
6323 __isl_take isl_map *map2);
6324 __isl_give isl_map *isl_map_apply_range(
6325 __isl_take isl_map *map1,
6326 __isl_take isl_map *map2);
6328 #include <isl/union_map.h>
6329 __isl_give isl_union_map *isl_union_map_apply_domain(
6330 __isl_take isl_union_map *umap1,
6331 __isl_take isl_union_map *umap2);
6332 __isl_give isl_union_map *isl_union_map_apply_range(
6333 __isl_take isl_union_map *umap1,
6334 __isl_take isl_union_map *umap2);
6336 #include <isl/aff.h>
6337 __isl_give isl_union_pw_aff *
6338 isl_multi_union_pw_aff_apply_aff(
6339 __isl_take isl_multi_union_pw_aff *mupa,
6340 __isl_take isl_aff *aff);
6341 __isl_give isl_union_pw_aff *
6342 isl_multi_union_pw_aff_apply_pw_aff(
6343 __isl_take isl_multi_union_pw_aff *mupa,
6344 __isl_take isl_pw_aff *pa);
6345 __isl_give isl_multi_union_pw_aff *
6346 isl_multi_union_pw_aff_apply_multi_aff(
6347 __isl_take isl_multi_union_pw_aff *mupa,
6348 __isl_take isl_multi_aff *ma);
6349 __isl_give isl_multi_union_pw_aff *
6350 isl_multi_union_pw_aff_apply_pw_multi_aff(
6351 __isl_take isl_multi_union_pw_aff *mupa,
6352 __isl_take isl_pw_multi_aff *pma);
6354 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6355 over the shared domain of the elements of the input. The dimension is
6356 required to be greater than zero.
6357 The C<isl_multi_union_pw_aff> argument of
6358 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6359 but only if the range of the C<isl_multi_aff> argument
6360 is also zero-dimensional.
6361 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6363 #include <isl/polynomial.h>
6364 __isl_give isl_pw_qpolynomial_fold *
6365 isl_set_apply_pw_qpolynomial_fold(
6366 __isl_take isl_set *set,
6367 __isl_take isl_pw_qpolynomial_fold *pwf,
6369 __isl_give isl_pw_qpolynomial_fold *
6370 isl_map_apply_pw_qpolynomial_fold(
6371 __isl_take isl_map *map,
6372 __isl_take isl_pw_qpolynomial_fold *pwf,
6374 __isl_give isl_union_pw_qpolynomial_fold *
6375 isl_union_set_apply_union_pw_qpolynomial_fold(
6376 __isl_take isl_union_set *uset,
6377 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6379 __isl_give isl_union_pw_qpolynomial_fold *
6380 isl_union_map_apply_union_pw_qpolynomial_fold(
6381 __isl_take isl_union_map *umap,
6382 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6385 The functions taking a map
6386 compose the given map with the given piecewise quasipolynomial reduction.
6387 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6388 over all elements in the intersection of the range of the map
6389 and the domain of the piecewise quasipolynomial reduction
6390 as a function of an element in the domain of the map.
6391 The functions taking a set compute a bound over all elements in the
6392 intersection of the set and the domain of the
6393 piecewise quasipolynomial reduction.
6397 #include <isl/set.h>
6398 __isl_give isl_basic_set *
6399 isl_basic_set_preimage_multi_aff(
6400 __isl_take isl_basic_set *bset,
6401 __isl_take isl_multi_aff *ma);
6402 __isl_give isl_set *isl_set_preimage_multi_aff(
6403 __isl_take isl_set *set,
6404 __isl_take isl_multi_aff *ma);
6405 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6406 __isl_take isl_set *set,
6407 __isl_take isl_pw_multi_aff *pma);
6408 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6409 __isl_take isl_set *set,
6410 __isl_take isl_multi_pw_aff *mpa);
6412 #include <isl/union_set.h>
6413 __isl_give isl_union_set *
6414 isl_union_set_preimage_multi_aff(
6415 __isl_take isl_union_set *uset,
6416 __isl_take isl_multi_aff *ma);
6417 __isl_give isl_union_set *
6418 isl_union_set_preimage_pw_multi_aff(
6419 __isl_take isl_union_set *uset,
6420 __isl_take isl_pw_multi_aff *pma);
6421 __isl_give isl_union_set *
6422 isl_union_set_preimage_union_pw_multi_aff(
6423 __isl_take isl_union_set *uset,
6424 __isl_take isl_union_pw_multi_aff *upma);
6426 #include <isl/map.h>
6427 __isl_give isl_basic_map *
6428 isl_basic_map_preimage_domain_multi_aff(
6429 __isl_take isl_basic_map *bmap,
6430 __isl_take isl_multi_aff *ma);
6431 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6432 __isl_take isl_map *map,
6433 __isl_take isl_multi_aff *ma);
6434 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6435 __isl_take isl_map *map,
6436 __isl_take isl_multi_aff *ma);
6437 __isl_give isl_map *
6438 isl_map_preimage_domain_pw_multi_aff(
6439 __isl_take isl_map *map,
6440 __isl_take isl_pw_multi_aff *pma);
6441 __isl_give isl_map *
6442 isl_map_preimage_range_pw_multi_aff(
6443 __isl_take isl_map *map,
6444 __isl_take isl_pw_multi_aff *pma);
6445 __isl_give isl_map *
6446 isl_map_preimage_domain_multi_pw_aff(
6447 __isl_take isl_map *map,
6448 __isl_take isl_multi_pw_aff *mpa);
6449 __isl_give isl_basic_map *
6450 isl_basic_map_preimage_range_multi_aff(
6451 __isl_take isl_basic_map *bmap,
6452 __isl_take isl_multi_aff *ma);
6454 #include <isl/union_map.h>
6455 __isl_give isl_union_map *
6456 isl_union_map_preimage_domain_multi_aff(
6457 __isl_take isl_union_map *umap,
6458 __isl_take isl_multi_aff *ma);
6459 __isl_give isl_union_map *
6460 isl_union_map_preimage_range_multi_aff(
6461 __isl_take isl_union_map *umap,
6462 __isl_take isl_multi_aff *ma);
6463 __isl_give isl_union_map *
6464 isl_union_map_preimage_domain_pw_multi_aff(
6465 __isl_take isl_union_map *umap,
6466 __isl_take isl_pw_multi_aff *pma);
6467 __isl_give isl_union_map *
6468 isl_union_map_preimage_range_pw_multi_aff(
6469 __isl_take isl_union_map *umap,
6470 __isl_take isl_pw_multi_aff *pma);
6471 __isl_give isl_union_map *
6472 isl_union_map_preimage_domain_union_pw_multi_aff(
6473 __isl_take isl_union_map *umap,
6474 __isl_take isl_union_pw_multi_aff *upma);
6475 __isl_give isl_union_map *
6476 isl_union_map_preimage_range_union_pw_multi_aff(
6477 __isl_take isl_union_map *umap,
6478 __isl_take isl_union_pw_multi_aff *upma);
6480 These functions compute the preimage of the given set or map domain/range under
6481 the given function. In other words, the expression is plugged
6482 into the set description or into the domain/range of the map.
6486 #include <isl/aff.h>
6487 __isl_give isl_aff *isl_aff_pullback_aff(
6488 __isl_take isl_aff *aff1,
6489 __isl_take isl_aff *aff2);
6490 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6491 __isl_take isl_aff *aff,
6492 __isl_take isl_multi_aff *ma);
6493 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6494 __isl_take isl_pw_aff *pa,
6495 __isl_take isl_multi_aff *ma);
6496 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6497 __isl_take isl_pw_aff *pa,
6498 __isl_take isl_pw_multi_aff *pma);
6499 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6500 __isl_take isl_pw_aff *pa,
6501 __isl_take isl_multi_pw_aff *mpa);
6502 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6503 __isl_take isl_multi_aff *ma1,
6504 __isl_take isl_multi_aff *ma2);
6505 __isl_give isl_pw_multi_aff *
6506 isl_pw_multi_aff_pullback_multi_aff(
6507 __isl_take isl_pw_multi_aff *pma,
6508 __isl_take isl_multi_aff *ma);
6509 __isl_give isl_multi_pw_aff *
6510 isl_multi_pw_aff_pullback_multi_aff(
6511 __isl_take isl_multi_pw_aff *mpa,
6512 __isl_take isl_multi_aff *ma);
6513 __isl_give isl_pw_multi_aff *
6514 isl_pw_multi_aff_pullback_pw_multi_aff(
6515 __isl_take isl_pw_multi_aff *pma1,
6516 __isl_take isl_pw_multi_aff *pma2);
6517 __isl_give isl_multi_pw_aff *
6518 isl_multi_pw_aff_pullback_pw_multi_aff(
6519 __isl_take isl_multi_pw_aff *mpa,
6520 __isl_take isl_pw_multi_aff *pma);
6521 __isl_give isl_multi_pw_aff *
6522 isl_multi_pw_aff_pullback_multi_pw_aff(
6523 __isl_take isl_multi_pw_aff *mpa1,
6524 __isl_take isl_multi_pw_aff *mpa2);
6525 __isl_give isl_union_pw_aff *
6526 isl_union_pw_aff_pullback_union_pw_multi_aff(
6527 __isl_take isl_union_pw_aff *upa,
6528 __isl_take isl_union_pw_multi_aff *upma);
6529 __isl_give isl_union_pw_multi_aff *
6530 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6531 __isl_take isl_union_pw_multi_aff *upma1,
6532 __isl_take isl_union_pw_multi_aff *upma2);
6533 __isl_give isl_multi_union_pw_aff *
6534 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6535 __isl_take isl_multi_union_pw_aff *mupa,
6536 __isl_take isl_union_pw_multi_aff *upma);
6538 These functions precompose the first expression by the second function.
6539 In other words, the second function is plugged
6540 into the first expression.
6544 #include <isl/aff.h>
6545 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6546 __isl_take isl_aff *aff1,
6547 __isl_take isl_aff *aff2);
6548 __isl_give isl_set *isl_aff_eq_set(
6549 __isl_take isl_aff *aff1,
6550 __isl_take isl_aff *aff2);
6551 __isl_give isl_set *isl_aff_ne_set(
6552 __isl_take isl_aff *aff1,
6553 __isl_take isl_aff *aff2);
6554 __isl_give isl_basic_set *isl_aff_le_basic_set(
6555 __isl_take isl_aff *aff1,
6556 __isl_take isl_aff *aff2);
6557 __isl_give isl_set *isl_aff_le_set(
6558 __isl_take isl_aff *aff1,
6559 __isl_take isl_aff *aff2);
6560 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6561 __isl_take isl_aff *aff1,
6562 __isl_take isl_aff *aff2);
6563 __isl_give isl_set *isl_aff_lt_set(
6564 __isl_take isl_aff *aff1,
6565 __isl_take isl_aff *aff2);
6566 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6567 __isl_take isl_aff *aff1,
6568 __isl_take isl_aff *aff2);
6569 __isl_give isl_set *isl_aff_ge_set(
6570 __isl_take isl_aff *aff1,
6571 __isl_take isl_aff *aff2);
6572 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6573 __isl_take isl_aff *aff1,
6574 __isl_take isl_aff *aff2);
6575 __isl_give isl_set *isl_aff_gt_set(
6576 __isl_take isl_aff *aff1,
6577 __isl_take isl_aff *aff2);
6578 __isl_give isl_set *isl_pw_aff_eq_set(
6579 __isl_take isl_pw_aff *pwaff1,
6580 __isl_take isl_pw_aff *pwaff2);
6581 __isl_give isl_set *isl_pw_aff_ne_set(
6582 __isl_take isl_pw_aff *pwaff1,
6583 __isl_take isl_pw_aff *pwaff2);
6584 __isl_give isl_set *isl_pw_aff_le_set(
6585 __isl_take isl_pw_aff *pwaff1,
6586 __isl_take isl_pw_aff *pwaff2);
6587 __isl_give isl_set *isl_pw_aff_lt_set(
6588 __isl_take isl_pw_aff *pwaff1,
6589 __isl_take isl_pw_aff *pwaff2);
6590 __isl_give isl_set *isl_pw_aff_ge_set(
6591 __isl_take isl_pw_aff *pwaff1,
6592 __isl_take isl_pw_aff *pwaff2);
6593 __isl_give isl_set *isl_pw_aff_gt_set(
6594 __isl_take isl_pw_aff *pwaff1,
6595 __isl_take isl_pw_aff *pwaff2);
6597 __isl_give isl_set *isl_multi_aff_lex_le_set(
6598 __isl_take isl_multi_aff *ma1,
6599 __isl_take isl_multi_aff *ma2);
6600 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6601 __isl_take isl_multi_aff *ma1,
6602 __isl_take isl_multi_aff *ma2);
6603 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6604 __isl_take isl_multi_aff *ma1,
6605 __isl_take isl_multi_aff *ma2);
6606 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6607 __isl_take isl_multi_aff *ma1,
6608 __isl_take isl_multi_aff *ma2);
6610 __isl_give isl_set *isl_pw_aff_list_eq_set(
6611 __isl_take isl_pw_aff_list *list1,
6612 __isl_take isl_pw_aff_list *list2);
6613 __isl_give isl_set *isl_pw_aff_list_ne_set(
6614 __isl_take isl_pw_aff_list *list1,
6615 __isl_take isl_pw_aff_list *list2);
6616 __isl_give isl_set *isl_pw_aff_list_le_set(
6617 __isl_take isl_pw_aff_list *list1,
6618 __isl_take isl_pw_aff_list *list2);
6619 __isl_give isl_set *isl_pw_aff_list_lt_set(
6620 __isl_take isl_pw_aff_list *list1,
6621 __isl_take isl_pw_aff_list *list2);
6622 __isl_give isl_set *isl_pw_aff_list_ge_set(
6623 __isl_take isl_pw_aff_list *list1,
6624 __isl_take isl_pw_aff_list *list2);
6625 __isl_give isl_set *isl_pw_aff_list_gt_set(
6626 __isl_take isl_pw_aff_list *list1,
6627 __isl_take isl_pw_aff_list *list2);
6629 The function C<isl_aff_ge_basic_set> returns a basic set
6630 containing those elements in the shared space
6631 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6632 The function C<isl_pw_aff_ge_set> returns a set
6633 containing those elements in the shared domain
6634 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6635 greater than or equal to C<pwaff2>.
6636 The function C<isl_multi_aff_lex_le_set> returns a set
6637 containing those elements in the shared domain space
6638 where C<ma1> is lexicographically smaller than or
6640 The functions operating on C<isl_pw_aff_list> apply the corresponding
6641 C<isl_pw_aff> function to each pair of elements in the two lists.
6643 #include <isl/aff.h>
6644 __isl_give isl_map *isl_pw_aff_eq_map(
6645 __isl_take isl_pw_aff *pa1,
6646 __isl_take isl_pw_aff *pa2);
6647 __isl_give isl_map *isl_pw_aff_lt_map(
6648 __isl_take isl_pw_aff *pa1,
6649 __isl_take isl_pw_aff *pa2);
6650 __isl_give isl_map *isl_pw_aff_gt_map(
6651 __isl_take isl_pw_aff *pa1,
6652 __isl_take isl_pw_aff *pa2);
6654 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6655 __isl_take isl_multi_pw_aff *mpa1,
6656 __isl_take isl_multi_pw_aff *mpa2);
6657 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6658 __isl_take isl_multi_pw_aff *mpa1,
6659 __isl_take isl_multi_pw_aff *mpa2);
6660 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6661 __isl_take isl_multi_pw_aff *mpa1,
6662 __isl_take isl_multi_pw_aff *mpa2);
6664 These functions return a map between domain elements of the arguments
6665 where the function values satisfy the given relation.
6667 #include <isl/union_map.h>
6668 __isl_give isl_union_map *
6669 isl_union_map_eq_at_multi_union_pw_aff(
6670 __isl_take isl_union_map *umap,
6671 __isl_take isl_multi_union_pw_aff *mupa);
6672 __isl_give isl_union_map *
6673 isl_union_map_lex_lt_at_multi_union_pw_aff(
6674 __isl_take isl_union_map *umap,
6675 __isl_take isl_multi_union_pw_aff *mupa);
6676 __isl_give isl_union_map *
6677 isl_union_map_lex_gt_at_multi_union_pw_aff(
6678 __isl_take isl_union_map *umap,
6679 __isl_take isl_multi_union_pw_aff *mupa);
6681 These functions select the subset of elements in the union map
6682 that have an equal or lexicographically smaller function value.
6684 =item * Cartesian Product
6686 #include <isl/space.h>
6687 __isl_give isl_space *isl_space_product(
6688 __isl_take isl_space *space1,
6689 __isl_take isl_space *space2);
6690 __isl_give isl_space *isl_space_domain_product(
6691 __isl_take isl_space *space1,
6692 __isl_take isl_space *space2);
6693 __isl_give isl_space *isl_space_range_product(
6694 __isl_take isl_space *space1,
6695 __isl_take isl_space *space2);
6698 C<isl_space_product>, C<isl_space_domain_product>
6699 and C<isl_space_range_product> take pairs or relation spaces and
6700 produce a single relations space, where either the domain, the range
6701 or both domain and range are wrapped spaces of relations between
6702 the domains and/or ranges of the input spaces.
6703 If the product is only constructed over the domain or the range
6704 then the ranges or the domains of the inputs should be the same.
6705 The function C<isl_space_product> also accepts a pair of set spaces,
6706 in which case it returns a wrapped space of a relation between the
6709 #include <isl/set.h>
6710 __isl_give isl_set *isl_set_product(
6711 __isl_take isl_set *set1,
6712 __isl_take isl_set *set2);
6714 #include <isl/map.h>
6715 __isl_give isl_basic_map *isl_basic_map_domain_product(
6716 __isl_take isl_basic_map *bmap1,
6717 __isl_take isl_basic_map *bmap2);
6718 __isl_give isl_basic_map *isl_basic_map_range_product(
6719 __isl_take isl_basic_map *bmap1,
6720 __isl_take isl_basic_map *bmap2);
6721 __isl_give isl_basic_map *isl_basic_map_product(
6722 __isl_take isl_basic_map *bmap1,
6723 __isl_take isl_basic_map *bmap2);
6724 __isl_give isl_map *isl_map_domain_product(
6725 __isl_take isl_map *map1,
6726 __isl_take isl_map *map2);
6727 __isl_give isl_map *isl_map_range_product(
6728 __isl_take isl_map *map1,
6729 __isl_take isl_map *map2);
6730 __isl_give isl_map *isl_map_product(
6731 __isl_take isl_map *map1,
6732 __isl_take isl_map *map2);
6734 #include <isl/union_set.h>
6735 __isl_give isl_union_set *isl_union_set_product(
6736 __isl_take isl_union_set *uset1,
6737 __isl_take isl_union_set *uset2);
6739 #include <isl/union_map.h>
6740 __isl_give isl_union_map *isl_union_map_domain_product(
6741 __isl_take isl_union_map *umap1,
6742 __isl_take isl_union_map *umap2);
6743 __isl_give isl_union_map *isl_union_map_range_product(
6744 __isl_take isl_union_map *umap1,
6745 __isl_take isl_union_map *umap2);
6746 __isl_give isl_union_map *isl_union_map_product(
6747 __isl_take isl_union_map *umap1,
6748 __isl_take isl_union_map *umap2);
6750 #include <isl/val.h>
6751 __isl_give isl_multi_val *isl_multi_val_range_product(
6752 __isl_take isl_multi_val *mv1,
6753 __isl_take isl_multi_val *mv2);
6754 __isl_give isl_multi_val *isl_multi_val_product(
6755 __isl_take isl_multi_val *mv1,
6756 __isl_take isl_multi_val *mv2);
6758 #include <isl/aff.h>
6759 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6760 __isl_take isl_multi_aff *ma1,
6761 __isl_take isl_multi_aff *ma2);
6762 __isl_give isl_multi_aff *isl_multi_aff_product(
6763 __isl_take isl_multi_aff *ma1,
6764 __isl_take isl_multi_aff *ma2);
6765 __isl_give isl_multi_pw_aff *
6766 isl_multi_pw_aff_range_product(
6767 __isl_take isl_multi_pw_aff *mpa1,
6768 __isl_take isl_multi_pw_aff *mpa2);
6769 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6770 __isl_take isl_multi_pw_aff *mpa1,
6771 __isl_take isl_multi_pw_aff *mpa2);
6772 __isl_give isl_pw_multi_aff *
6773 isl_pw_multi_aff_range_product(
6774 __isl_take isl_pw_multi_aff *pma1,
6775 __isl_take isl_pw_multi_aff *pma2);
6776 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6777 __isl_take isl_pw_multi_aff *pma1,
6778 __isl_take isl_pw_multi_aff *pma2);
6779 __isl_give isl_multi_union_pw_aff *
6780 isl_multi_union_pw_aff_range_product(
6781 __isl_take isl_multi_union_pw_aff *mupa1,
6782 __isl_take isl_multi_union_pw_aff *mupa2);
6784 The above functions compute the cross product of the given
6785 sets, relations or functions. The domains and ranges of the results
6786 are wrapped maps between domains and ranges of the inputs.
6787 To obtain a ``flat'' product, use the following functions
6790 #include <isl/set.h>
6791 __isl_give isl_basic_set *isl_basic_set_flat_product(
6792 __isl_take isl_basic_set *bset1,
6793 __isl_take isl_basic_set *bset2);
6794 __isl_give isl_set *isl_set_flat_product(
6795 __isl_take isl_set *set1,
6796 __isl_take isl_set *set2);
6798 #include <isl/map.h>
6799 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6800 __isl_take isl_basic_map *bmap1,
6801 __isl_take isl_basic_map *bmap2);
6802 __isl_give isl_map *isl_map_flat_domain_product(
6803 __isl_take isl_map *map1,
6804 __isl_take isl_map *map2);
6805 __isl_give isl_map *isl_map_flat_range_product(
6806 __isl_take isl_map *map1,
6807 __isl_take isl_map *map2);
6808 __isl_give isl_basic_map *isl_basic_map_flat_product(
6809 __isl_take isl_basic_map *bmap1,
6810 __isl_take isl_basic_map *bmap2);
6811 __isl_give isl_map *isl_map_flat_product(
6812 __isl_take isl_map *map1,
6813 __isl_take isl_map *map2);
6815 #include <isl/union_map.h>
6816 __isl_give isl_union_map *
6817 isl_union_map_flat_domain_product(
6818 __isl_take isl_union_map *umap1,
6819 __isl_take isl_union_map *umap2);
6820 __isl_give isl_union_map *
6821 isl_union_map_flat_range_product(
6822 __isl_take isl_union_map *umap1,
6823 __isl_take isl_union_map *umap2);
6825 #include <isl/val.h>
6826 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6827 __isl_take isl_multi_val *mv1,
6828 __isl_take isl_multi_aff *mv2);
6830 #include <isl/aff.h>
6831 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6832 __isl_take isl_multi_aff *ma1,
6833 __isl_take isl_multi_aff *ma2);
6834 __isl_give isl_pw_multi_aff *
6835 isl_pw_multi_aff_flat_range_product(
6836 __isl_take isl_pw_multi_aff *pma1,
6837 __isl_take isl_pw_multi_aff *pma2);
6838 __isl_give isl_multi_pw_aff *
6839 isl_multi_pw_aff_flat_range_product(
6840 __isl_take isl_multi_pw_aff *mpa1,
6841 __isl_take isl_multi_pw_aff *mpa2);
6842 __isl_give isl_union_pw_multi_aff *
6843 isl_union_pw_multi_aff_flat_range_product(
6844 __isl_take isl_union_pw_multi_aff *upma1,
6845 __isl_take isl_union_pw_multi_aff *upma2);
6846 __isl_give isl_multi_union_pw_aff *
6847 isl_multi_union_pw_aff_flat_range_product(
6848 __isl_take isl_multi_union_pw_aff *mupa1,
6849 __isl_take isl_multi_union_pw_aff *mupa2);
6851 #include <isl/space.h>
6852 __isl_give isl_space *isl_space_factor_domain(
6853 __isl_take isl_space *space);
6854 __isl_give isl_space *isl_space_factor_range(
6855 __isl_take isl_space *space);
6856 __isl_give isl_space *isl_space_domain_factor_domain(
6857 __isl_take isl_space *space);
6858 __isl_give isl_space *isl_space_domain_factor_range(
6859 __isl_take isl_space *space);
6860 __isl_give isl_space *isl_space_range_factor_domain(
6861 __isl_take isl_space *space);
6862 __isl_give isl_space *isl_space_range_factor_range(
6863 __isl_take isl_space *space);
6865 The functions C<isl_space_range_factor_domain> and
6866 C<isl_space_range_factor_range> extract the two arguments from
6867 the result of a call to C<isl_space_range_product>.
6869 The arguments of a call to a product can be extracted
6870 from the result using the following functions.
6872 #include <isl/map.h>
6873 __isl_give isl_map *isl_map_factor_domain(
6874 __isl_take isl_map *map);
6875 __isl_give isl_map *isl_map_factor_range(
6876 __isl_take isl_map *map);
6877 __isl_give isl_map *isl_map_domain_factor_domain(
6878 __isl_take isl_map *map);
6879 __isl_give isl_map *isl_map_domain_factor_range(
6880 __isl_take isl_map *map);
6881 __isl_give isl_map *isl_map_range_factor_domain(
6882 __isl_take isl_map *map);
6883 __isl_give isl_map *isl_map_range_factor_range(
6884 __isl_take isl_map *map);
6886 #include <isl/union_map.h>
6887 __isl_give isl_union_map *isl_union_map_factor_domain(
6888 __isl_take isl_union_map *umap);
6889 __isl_give isl_union_map *isl_union_map_factor_range(
6890 __isl_take isl_union_map *umap);
6891 __isl_give isl_union_map *
6892 isl_union_map_domain_factor_domain(
6893 __isl_take isl_union_map *umap);
6894 __isl_give isl_union_map *
6895 isl_union_map_domain_factor_range(
6896 __isl_take isl_union_map *umap);
6897 __isl_give isl_union_map *
6898 isl_union_map_range_factor_domain(
6899 __isl_take isl_union_map *umap);
6900 __isl_give isl_union_map *
6901 isl_union_map_range_factor_range(
6902 __isl_take isl_union_map *umap);
6904 #include <isl/val.h>
6905 __isl_give isl_multi_val *isl_multi_val_factor_range(
6906 __isl_take isl_multi_val *mv);
6907 __isl_give isl_multi_val *
6908 isl_multi_val_range_factor_domain(
6909 __isl_take isl_multi_val *mv);
6910 __isl_give isl_multi_val *
6911 isl_multi_val_range_factor_range(
6912 __isl_take isl_multi_val *mv);
6914 #include <isl/aff.h>
6915 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6916 __isl_take isl_multi_aff *ma);
6917 __isl_give isl_multi_aff *
6918 isl_multi_aff_range_factor_domain(
6919 __isl_take isl_multi_aff *ma);
6920 __isl_give isl_multi_aff *
6921 isl_multi_aff_range_factor_range(
6922 __isl_take isl_multi_aff *ma);
6923 __isl_give isl_multi_pw_aff *
6924 isl_multi_pw_aff_factor_range(
6925 __isl_take isl_multi_pw_aff *mpa);
6926 __isl_give isl_multi_pw_aff *
6927 isl_multi_pw_aff_range_factor_domain(
6928 __isl_take isl_multi_pw_aff *mpa);
6929 __isl_give isl_multi_pw_aff *
6930 isl_multi_pw_aff_range_factor_range(
6931 __isl_take isl_multi_pw_aff *mpa);
6932 __isl_give isl_multi_union_pw_aff *
6933 isl_multi_union_pw_aff_factor_range(
6934 __isl_take isl_multi_union_pw_aff *mupa);
6935 __isl_give isl_multi_union_pw_aff *
6936 isl_multi_union_pw_aff_range_factor_domain(
6937 __isl_take isl_multi_union_pw_aff *mupa);
6938 __isl_give isl_multi_union_pw_aff *
6939 isl_multi_union_pw_aff_range_factor_range(
6940 __isl_take isl_multi_union_pw_aff *mupa);
6942 The splice functions are a generalization of the flat product functions,
6943 where the second argument may be inserted at any position inside
6944 the first argument rather than being placed at the end.
6945 The functions C<isl_multi_val_factor_range>,
6946 C<isl_multi_aff_factor_range>,
6947 C<isl_multi_pw_aff_factor_range> and
6948 C<isl_multi_union_pw_aff_factor_range>
6949 take functions that live in a set space.
6951 #include <isl/val.h>
6952 __isl_give isl_multi_val *isl_multi_val_range_splice(
6953 __isl_take isl_multi_val *mv1, unsigned pos,
6954 __isl_take isl_multi_val *mv2);
6956 #include <isl/aff.h>
6957 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6958 __isl_take isl_multi_aff *ma1, unsigned pos,
6959 __isl_take isl_multi_aff *ma2);
6960 __isl_give isl_multi_aff *isl_multi_aff_splice(
6961 __isl_take isl_multi_aff *ma1,
6962 unsigned in_pos, unsigned out_pos,
6963 __isl_take isl_multi_aff *ma2);
6964 __isl_give isl_multi_pw_aff *
6965 isl_multi_pw_aff_range_splice(
6966 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6967 __isl_take isl_multi_pw_aff *mpa2);
6968 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6969 __isl_take isl_multi_pw_aff *mpa1,
6970 unsigned in_pos, unsigned out_pos,
6971 __isl_take isl_multi_pw_aff *mpa2);
6972 __isl_give isl_multi_union_pw_aff *
6973 isl_multi_union_pw_aff_range_splice(
6974 __isl_take isl_multi_union_pw_aff *mupa1,
6976 __isl_take isl_multi_union_pw_aff *mupa2);
6978 =item * Simplification
6980 When applied to a set or relation,
6981 the gist operation returns a set or relation that has the
6982 same intersection with the context as the input set or relation.
6983 Any implicit equality in the intersection is made explicit in the result,
6984 while all inequalities that are redundant with respect to the intersection
6986 In case of union sets and relations, the gist operation is performed
6989 When applied to a function,
6990 the gist operation applies the set gist operation to each of
6991 the cells in the domain of the input piecewise expression.
6992 The context is also exploited
6993 to simplify the expression associated to each cell.
6995 #include <isl/set.h>
6996 __isl_give isl_basic_set *isl_basic_set_gist(
6997 __isl_take isl_basic_set *bset,
6998 __isl_take isl_basic_set *context);
6999 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
7000 __isl_take isl_set *context);
7001 __isl_give isl_set *isl_set_gist_params(
7002 __isl_take isl_set *set,
7003 __isl_take isl_set *context);
7005 #include <isl/map.h>
7006 __isl_give isl_basic_map *isl_basic_map_gist(
7007 __isl_take isl_basic_map *bmap,
7008 __isl_take isl_basic_map *context);
7009 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7010 __isl_take isl_basic_map *bmap,
7011 __isl_take isl_basic_set *context);
7012 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7013 __isl_take isl_map *context);
7014 __isl_give isl_map *isl_map_gist_params(
7015 __isl_take isl_map *map,
7016 __isl_take isl_set *context);
7017 __isl_give isl_map *isl_map_gist_domain(
7018 __isl_take isl_map *map,
7019 __isl_take isl_set *context);
7020 __isl_give isl_map *isl_map_gist_range(
7021 __isl_take isl_map *map,
7022 __isl_take isl_set *context);
7024 #include <isl/union_set.h>
7025 __isl_give isl_union_set *isl_union_set_gist(
7026 __isl_take isl_union_set *uset,
7027 __isl_take isl_union_set *context);
7028 __isl_give isl_union_set *isl_union_set_gist_params(
7029 __isl_take isl_union_set *uset,
7030 __isl_take isl_set *set);
7032 #include <isl/union_map.h>
7033 __isl_give isl_union_map *isl_union_map_gist(
7034 __isl_take isl_union_map *umap,
7035 __isl_take isl_union_map *context);
7036 __isl_give isl_union_map *isl_union_map_gist_params(
7037 __isl_take isl_union_map *umap,
7038 __isl_take isl_set *set);
7039 __isl_give isl_union_map *isl_union_map_gist_domain(
7040 __isl_take isl_union_map *umap,
7041 __isl_take isl_union_set *uset);
7042 __isl_give isl_union_map *isl_union_map_gist_range(
7043 __isl_take isl_union_map *umap,
7044 __isl_take isl_union_set *uset);
7046 #include <isl/aff.h>
7047 __isl_give isl_aff *isl_aff_gist_params(
7048 __isl_take isl_aff *aff,
7049 __isl_take isl_set *context);
7050 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7051 __isl_take isl_set *context);
7052 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7053 __isl_take isl_multi_aff *maff,
7054 __isl_take isl_set *context);
7055 __isl_give isl_multi_aff *isl_multi_aff_gist(
7056 __isl_take isl_multi_aff *maff,
7057 __isl_take isl_set *context);
7058 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7059 __isl_take isl_pw_aff *pwaff,
7060 __isl_take isl_set *context);
7061 __isl_give isl_pw_aff *isl_pw_aff_gist(
7062 __isl_take isl_pw_aff *pwaff,
7063 __isl_take isl_set *context);
7064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7065 __isl_take isl_pw_multi_aff *pma,
7066 __isl_take isl_set *set);
7067 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7068 __isl_take isl_pw_multi_aff *pma,
7069 __isl_take isl_set *set);
7070 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7071 __isl_take isl_multi_pw_aff *mpa,
7072 __isl_take isl_set *set);
7073 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7074 __isl_take isl_multi_pw_aff *mpa,
7075 __isl_take isl_set *set);
7076 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7077 __isl_take isl_union_pw_aff *upa,
7078 __isl_take isl_union_set *context);
7079 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7080 __isl_take isl_union_pw_aff *upa,
7081 __isl_take isl_set *context);
7082 __isl_give isl_union_pw_multi_aff *
7083 isl_union_pw_multi_aff_gist_params(
7084 __isl_take isl_union_pw_multi_aff *upma,
7085 __isl_take isl_set *context);
7086 __isl_give isl_union_pw_multi_aff *
7087 isl_union_pw_multi_aff_gist(
7088 __isl_take isl_union_pw_multi_aff *upma,
7089 __isl_take isl_union_set *context);
7090 __isl_give isl_multi_union_pw_aff *
7091 isl_multi_union_pw_aff_gist_params(
7092 __isl_take isl_multi_union_pw_aff *aff,
7093 __isl_take isl_set *context);
7094 __isl_give isl_multi_union_pw_aff *
7095 isl_multi_union_pw_aff_gist(
7096 __isl_take isl_multi_union_pw_aff *aff,
7097 __isl_take isl_union_set *context);
7099 #include <isl/polynomial.h>
7100 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7101 __isl_take isl_qpolynomial *qp,
7102 __isl_take isl_set *context);
7103 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7104 __isl_take isl_qpolynomial *qp,
7105 __isl_take isl_set *context);
7106 __isl_give isl_qpolynomial_fold *
7107 isl_qpolynomial_fold_gist_params(
7108 __isl_take isl_qpolynomial_fold *fold,
7109 __isl_take isl_set *context);
7110 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7111 __isl_take isl_qpolynomial_fold *fold,
7112 __isl_take isl_set *context);
7113 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7114 __isl_take isl_pw_qpolynomial *pwqp,
7115 __isl_take isl_set *context);
7116 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7117 __isl_take isl_pw_qpolynomial *pwqp,
7118 __isl_take isl_set *context);
7119 __isl_give isl_pw_qpolynomial_fold *
7120 isl_pw_qpolynomial_fold_gist(
7121 __isl_take isl_pw_qpolynomial_fold *pwf,
7122 __isl_take isl_set *context);
7123 __isl_give isl_pw_qpolynomial_fold *
7124 isl_pw_qpolynomial_fold_gist_params(
7125 __isl_take isl_pw_qpolynomial_fold *pwf,
7126 __isl_take isl_set *context);
7127 __isl_give isl_union_pw_qpolynomial *
7128 isl_union_pw_qpolynomial_gist_params(
7129 __isl_take isl_union_pw_qpolynomial *upwqp,
7130 __isl_take isl_set *context);
7131 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7132 __isl_take isl_union_pw_qpolynomial *upwqp,
7133 __isl_take isl_union_set *context);
7134 __isl_give isl_union_pw_qpolynomial_fold *
7135 isl_union_pw_qpolynomial_fold_gist(
7136 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7137 __isl_take isl_union_set *context);
7138 __isl_give isl_union_pw_qpolynomial_fold *
7139 isl_union_pw_qpolynomial_fold_gist_params(
7140 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7141 __isl_take isl_set *context);
7143 =item * Binary Arithmetic Operations
7145 #include <isl/set.h>
7146 __isl_give isl_set *isl_set_sum(
7147 __isl_take isl_set *set1,
7148 __isl_take isl_set *set2);
7149 #include <isl/map.h>
7150 __isl_give isl_map *isl_map_sum(
7151 __isl_take isl_map *map1,
7152 __isl_take isl_map *map2);
7154 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7155 i.e., the set containing the sums of pairs of elements from
7156 C<set1> and C<set2>.
7157 The domain of the result of C<isl_map_sum> is the intersection
7158 of the domains of its two arguments. The corresponding range
7159 elements are the sums of the corresponding range elements
7160 in the two arguments.
7162 #include <isl/val.h>
7163 __isl_give isl_multi_val *isl_multi_val_add(
7164 __isl_take isl_multi_val *mv1,
7165 __isl_take isl_multi_val *mv2);
7166 __isl_give isl_multi_val *isl_multi_val_sub(
7167 __isl_take isl_multi_val *mv1,
7168 __isl_take isl_multi_val *mv2);
7170 #include <isl/aff.h>
7171 __isl_give isl_aff *isl_aff_add(
7172 __isl_take isl_aff *aff1,
7173 __isl_take isl_aff *aff2);
7174 __isl_give isl_multi_aff *isl_multi_aff_add(
7175 __isl_take isl_multi_aff *maff1,
7176 __isl_take isl_multi_aff *maff2);
7177 __isl_give isl_pw_aff *isl_pw_aff_add(
7178 __isl_take isl_pw_aff *pwaff1,
7179 __isl_take isl_pw_aff *pwaff2);
7180 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7181 __isl_take isl_multi_pw_aff *mpa1,
7182 __isl_take isl_multi_pw_aff *mpa2);
7183 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7184 __isl_take isl_pw_multi_aff *pma1,
7185 __isl_take isl_pw_multi_aff *pma2);
7186 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7187 __isl_take isl_union_pw_aff *upa1,
7188 __isl_take isl_union_pw_aff *upa2);
7189 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7190 __isl_take isl_union_pw_multi_aff *upma1,
7191 __isl_take isl_union_pw_multi_aff *upma2);
7192 __isl_give isl_multi_union_pw_aff *
7193 isl_multi_union_pw_aff_add(
7194 __isl_take isl_multi_union_pw_aff *mupa1,
7195 __isl_take isl_multi_union_pw_aff *mupa2);
7196 __isl_give isl_pw_aff *isl_pw_aff_min(
7197 __isl_take isl_pw_aff *pwaff1,
7198 __isl_take isl_pw_aff *pwaff2);
7199 __isl_give isl_pw_aff *isl_pw_aff_max(
7200 __isl_take isl_pw_aff *pwaff1,
7201 __isl_take isl_pw_aff *pwaff2);
7202 __isl_give isl_aff *isl_aff_sub(
7203 __isl_take isl_aff *aff1,
7204 __isl_take isl_aff *aff2);
7205 __isl_give isl_multi_aff *isl_multi_aff_sub(
7206 __isl_take isl_multi_aff *ma1,
7207 __isl_take isl_multi_aff *ma2);
7208 __isl_give isl_pw_aff *isl_pw_aff_sub(
7209 __isl_take isl_pw_aff *pwaff1,
7210 __isl_take isl_pw_aff *pwaff2);
7211 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7212 __isl_take isl_multi_pw_aff *mpa1,
7213 __isl_take isl_multi_pw_aff *mpa2);
7214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7215 __isl_take isl_pw_multi_aff *pma1,
7216 __isl_take isl_pw_multi_aff *pma2);
7217 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7218 __isl_take isl_union_pw_aff *upa1,
7219 __isl_take isl_union_pw_aff *upa2);
7220 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7221 __isl_take isl_union_pw_multi_aff *upma1,
7222 __isl_take isl_union_pw_multi_aff *upma2);
7223 __isl_give isl_multi_union_pw_aff *
7224 isl_multi_union_pw_aff_sub(
7225 __isl_take isl_multi_union_pw_aff *mupa1,
7226 __isl_take isl_multi_union_pw_aff *mupa2);
7228 C<isl_aff_sub> subtracts the second argument from the first.
7230 #include <isl/polynomial.h>
7231 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7232 __isl_take isl_qpolynomial *qp1,
7233 __isl_take isl_qpolynomial *qp2);
7234 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7235 __isl_take isl_pw_qpolynomial *pwqp1,
7236 __isl_take isl_pw_qpolynomial *pwqp2);
7237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7238 __isl_take isl_pw_qpolynomial *pwqp1,
7239 __isl_take isl_pw_qpolynomial *pwqp2);
7240 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7241 __isl_take isl_pw_qpolynomial_fold *pwf1,
7242 __isl_take isl_pw_qpolynomial_fold *pwf2);
7243 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7244 __isl_take isl_union_pw_qpolynomial *upwqp1,
7245 __isl_take isl_union_pw_qpolynomial *upwqp2);
7246 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7247 __isl_take isl_qpolynomial *qp1,
7248 __isl_take isl_qpolynomial *qp2);
7249 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7250 __isl_take isl_pw_qpolynomial *pwqp1,
7251 __isl_take isl_pw_qpolynomial *pwqp2);
7252 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7253 __isl_take isl_union_pw_qpolynomial *upwqp1,
7254 __isl_take isl_union_pw_qpolynomial *upwqp2);
7255 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7256 __isl_take isl_pw_qpolynomial_fold *pwf1,
7257 __isl_take isl_pw_qpolynomial_fold *pwf2);
7258 __isl_give isl_union_pw_qpolynomial_fold *
7259 isl_union_pw_qpolynomial_fold_fold(
7260 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7261 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7263 #include <isl/aff.h>
7264 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7265 __isl_take isl_pw_aff *pwaff1,
7266 __isl_take isl_pw_aff *pwaff2);
7267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7268 __isl_take isl_pw_multi_aff *pma1,
7269 __isl_take isl_pw_multi_aff *pma2);
7270 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7271 __isl_take isl_union_pw_aff *upa1,
7272 __isl_take isl_union_pw_aff *upa2);
7273 __isl_give isl_union_pw_multi_aff *
7274 isl_union_pw_multi_aff_union_add(
7275 __isl_take isl_union_pw_multi_aff *upma1,
7276 __isl_take isl_union_pw_multi_aff *upma2);
7277 __isl_give isl_multi_union_pw_aff *
7278 isl_multi_union_pw_aff_union_add(
7279 __isl_take isl_multi_union_pw_aff *mupa1,
7280 __isl_take isl_multi_union_pw_aff *mupa2);
7281 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7282 __isl_take isl_pw_aff *pwaff1,
7283 __isl_take isl_pw_aff *pwaff2);
7284 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7285 __isl_take isl_pw_aff *pwaff1,
7286 __isl_take isl_pw_aff *pwaff2);
7288 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7289 expression with a domain that is the union of those of C<pwaff1> and
7290 C<pwaff2> and such that on each cell, the quasi-affine expression is
7291 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7292 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7293 associated expression is the defined one.
7294 This in contrast to the C<isl_pw_aff_max> function, which is
7295 only defined on the shared definition domain of the arguments.
7297 #include <isl/val.h>
7298 __isl_give isl_multi_val *isl_multi_val_add_val(
7299 __isl_take isl_multi_val *mv,
7300 __isl_take isl_val *v);
7301 __isl_give isl_multi_val *isl_multi_val_mod_val(
7302 __isl_take isl_multi_val *mv,
7303 __isl_take isl_val *v);
7304 __isl_give isl_multi_val *isl_multi_val_scale_val(
7305 __isl_take isl_multi_val *mv,
7306 __isl_take isl_val *v);
7307 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7308 __isl_take isl_multi_val *mv,
7309 __isl_take isl_val *v);
7311 #include <isl/aff.h>
7312 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7313 __isl_take isl_val *mod);
7314 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7315 __isl_take isl_pw_aff *pa,
7316 __isl_take isl_val *mod);
7317 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7318 __isl_take isl_union_pw_aff *upa,
7319 __isl_take isl_val *f);
7320 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7321 __isl_take isl_val *v);
7322 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7323 __isl_take isl_multi_aff *ma,
7324 __isl_take isl_val *v);
7325 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7326 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7327 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7328 __isl_take isl_multi_pw_aff *mpa,
7329 __isl_take isl_val *v);
7330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7331 __isl_take isl_pw_multi_aff *pma,
7332 __isl_take isl_val *v);
7333 __isl_give isl_union_pw_multi_aff *
7334 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7335 __isl_take isl_union_pw_aff *upa,
7336 __isl_take isl_val *f);
7337 isl_union_pw_multi_aff_scale_val(
7338 __isl_take isl_union_pw_multi_aff *upma,
7339 __isl_take isl_val *val);
7340 __isl_give isl_multi_union_pw_aff *
7341 isl_multi_union_pw_aff_scale_val(
7342 __isl_take isl_multi_union_pw_aff *mupa,
7343 __isl_take isl_val *v);
7344 __isl_give isl_aff *isl_aff_scale_down_ui(
7345 __isl_take isl_aff *aff, unsigned f);
7346 __isl_give isl_aff *isl_aff_scale_down_val(
7347 __isl_take isl_aff *aff, __isl_take isl_val *v);
7348 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7349 __isl_take isl_multi_aff *ma,
7350 __isl_take isl_val *v);
7351 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7352 __isl_take isl_pw_aff *pa,
7353 __isl_take isl_val *f);
7354 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7355 __isl_take isl_multi_pw_aff *mpa,
7356 __isl_take isl_val *v);
7357 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7358 __isl_take isl_pw_multi_aff *pma,
7359 __isl_take isl_val *v);
7360 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7361 __isl_take isl_union_pw_aff *upa,
7362 __isl_take isl_val *v);
7363 __isl_give isl_union_pw_multi_aff *
7364 isl_union_pw_multi_aff_scale_down_val(
7365 __isl_take isl_union_pw_multi_aff *upma,
7366 __isl_take isl_val *val);
7367 __isl_give isl_multi_union_pw_aff *
7368 isl_multi_union_pw_aff_scale_down_val(
7369 __isl_take isl_multi_union_pw_aff *mupa,
7370 __isl_take isl_val *v);
7372 #include <isl/polynomial.h>
7373 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7374 __isl_take isl_qpolynomial *qp,
7375 __isl_take isl_val *v);
7376 __isl_give isl_qpolynomial_fold *
7377 isl_qpolynomial_fold_scale_val(
7378 __isl_take isl_qpolynomial_fold *fold,
7379 __isl_take isl_val *v);
7380 __isl_give isl_pw_qpolynomial *
7381 isl_pw_qpolynomial_scale_val(
7382 __isl_take isl_pw_qpolynomial *pwqp,
7383 __isl_take isl_val *v);
7384 __isl_give isl_pw_qpolynomial_fold *
7385 isl_pw_qpolynomial_fold_scale_val(
7386 __isl_take isl_pw_qpolynomial_fold *pwf,
7387 __isl_take isl_val *v);
7388 __isl_give isl_union_pw_qpolynomial *
7389 isl_union_pw_qpolynomial_scale_val(
7390 __isl_take isl_union_pw_qpolynomial *upwqp,
7391 __isl_take isl_val *v);
7392 __isl_give isl_union_pw_qpolynomial_fold *
7393 isl_union_pw_qpolynomial_fold_scale_val(
7394 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7395 __isl_take isl_val *v);
7396 __isl_give isl_qpolynomial *
7397 isl_qpolynomial_scale_down_val(
7398 __isl_take isl_qpolynomial *qp,
7399 __isl_take isl_val *v);
7400 __isl_give isl_qpolynomial_fold *
7401 isl_qpolynomial_fold_scale_down_val(
7402 __isl_take isl_qpolynomial_fold *fold,
7403 __isl_take isl_val *v);
7404 __isl_give isl_pw_qpolynomial *
7405 isl_pw_qpolynomial_scale_down_val(
7406 __isl_take isl_pw_qpolynomial *pwqp,
7407 __isl_take isl_val *v);
7408 __isl_give isl_pw_qpolynomial_fold *
7409 isl_pw_qpolynomial_fold_scale_down_val(
7410 __isl_take isl_pw_qpolynomial_fold *pwf,
7411 __isl_take isl_val *v);
7412 __isl_give isl_union_pw_qpolynomial *
7413 isl_union_pw_qpolynomial_scale_down_val(
7414 __isl_take isl_union_pw_qpolynomial *upwqp,
7415 __isl_take isl_val *v);
7416 __isl_give isl_union_pw_qpolynomial_fold *
7417 isl_union_pw_qpolynomial_fold_scale_down_val(
7418 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7419 __isl_take isl_val *v);
7421 #include <isl/val.h>
7422 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7423 __isl_take isl_multi_val *mv1,
7424 __isl_take isl_multi_val *mv2);
7425 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7426 __isl_take isl_multi_val *mv1,
7427 __isl_take isl_multi_val *mv2);
7428 __isl_give isl_multi_val *
7429 isl_multi_val_scale_down_multi_val(
7430 __isl_take isl_multi_val *mv1,
7431 __isl_take isl_multi_val *mv2);
7433 #include <isl/aff.h>
7434 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7435 __isl_take isl_multi_aff *ma,
7436 __isl_take isl_multi_val *mv);
7437 __isl_give isl_multi_union_pw_aff *
7438 isl_multi_union_pw_aff_mod_multi_val(
7439 __isl_take isl_multi_union_pw_aff *upma,
7440 __isl_take isl_multi_val *mv);
7441 __isl_give isl_multi_pw_aff *
7442 isl_multi_pw_aff_mod_multi_val(
7443 __isl_take isl_multi_pw_aff *mpa,
7444 __isl_take isl_multi_val *mv);
7445 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7446 __isl_take isl_multi_aff *ma,
7447 __isl_take isl_multi_val *mv);
7448 __isl_give isl_pw_multi_aff *
7449 isl_pw_multi_aff_scale_multi_val(
7450 __isl_take isl_pw_multi_aff *pma,
7451 __isl_take isl_multi_val *mv);
7452 __isl_give isl_multi_pw_aff *
7453 isl_multi_pw_aff_scale_multi_val(
7454 __isl_take isl_multi_pw_aff *mpa,
7455 __isl_take isl_multi_val *mv);
7456 __isl_give isl_multi_union_pw_aff *
7457 isl_multi_union_pw_aff_scale_multi_val(
7458 __isl_take isl_multi_union_pw_aff *mupa,
7459 __isl_take isl_multi_val *mv);
7460 __isl_give isl_union_pw_multi_aff *
7461 isl_union_pw_multi_aff_scale_multi_val(
7462 __isl_take isl_union_pw_multi_aff *upma,
7463 __isl_take isl_multi_val *mv);
7464 __isl_give isl_multi_aff *
7465 isl_multi_aff_scale_down_multi_val(
7466 __isl_take isl_multi_aff *ma,
7467 __isl_take isl_multi_val *mv);
7468 __isl_give isl_multi_pw_aff *
7469 isl_multi_pw_aff_scale_down_multi_val(
7470 __isl_take isl_multi_pw_aff *mpa,
7471 __isl_take isl_multi_val *mv);
7472 __isl_give isl_multi_union_pw_aff *
7473 isl_multi_union_pw_aff_scale_down_multi_val(
7474 __isl_take isl_multi_union_pw_aff *mupa,
7475 __isl_take isl_multi_val *mv);
7477 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7478 by the corresponding elements of C<mv>.
7480 #include <isl/aff.h>
7481 __isl_give isl_aff *isl_aff_mul(
7482 __isl_take isl_aff *aff1,
7483 __isl_take isl_aff *aff2);
7484 __isl_give isl_aff *isl_aff_div(
7485 __isl_take isl_aff *aff1,
7486 __isl_take isl_aff *aff2);
7487 __isl_give isl_pw_aff *isl_pw_aff_mul(
7488 __isl_take isl_pw_aff *pwaff1,
7489 __isl_take isl_pw_aff *pwaff2);
7490 __isl_give isl_pw_aff *isl_pw_aff_div(
7491 __isl_take isl_pw_aff *pa1,
7492 __isl_take isl_pw_aff *pa2);
7493 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7494 __isl_take isl_pw_aff *pa1,
7495 __isl_take isl_pw_aff *pa2);
7496 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7497 __isl_take isl_pw_aff *pa1,
7498 __isl_take isl_pw_aff *pa2);
7500 When multiplying two affine expressions, at least one of the two needs
7501 to be a constant. Similarly, when dividing an affine expression by another,
7502 the second expression needs to be a constant.
7503 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7504 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7507 #include <isl/polynomial.h>
7508 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7509 __isl_take isl_qpolynomial *qp1,
7510 __isl_take isl_qpolynomial *qp2);
7511 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7512 __isl_take isl_pw_qpolynomial *pwqp1,
7513 __isl_take isl_pw_qpolynomial *pwqp2);
7514 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7515 __isl_take isl_union_pw_qpolynomial *upwqp1,
7516 __isl_take isl_union_pw_qpolynomial *upwqp2);
7520 =head3 Lexicographic Optimization
7522 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7523 the following functions
7524 compute a set that contains the lexicographic minimum or maximum
7525 of the elements in C<set> (or C<bset>) for those values of the parameters
7526 that satisfy C<dom>.
7527 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7528 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7530 In other words, the union of the parameter values
7531 for which the result is non-empty and of C<*empty>
7534 #include <isl/set.h>
7535 __isl_give isl_set *isl_basic_set_partial_lexmin(
7536 __isl_take isl_basic_set *bset,
7537 __isl_take isl_basic_set *dom,
7538 __isl_give isl_set **empty);
7539 __isl_give isl_set *isl_basic_set_partial_lexmax(
7540 __isl_take isl_basic_set *bset,
7541 __isl_take isl_basic_set *dom,
7542 __isl_give isl_set **empty);
7543 __isl_give isl_set *isl_set_partial_lexmin(
7544 __isl_take isl_set *set, __isl_take isl_set *dom,
7545 __isl_give isl_set **empty);
7546 __isl_give isl_set *isl_set_partial_lexmax(
7547 __isl_take isl_set *set, __isl_take isl_set *dom,
7548 __isl_give isl_set **empty);
7550 Given a (basic) set C<set> (or C<bset>), the following functions simply
7551 return a set containing the lexicographic minimum or maximum
7552 of the elements in C<set> (or C<bset>).
7553 In case of union sets, the optimum is computed per space.
7555 #include <isl/set.h>
7556 __isl_give isl_set *isl_basic_set_lexmin(
7557 __isl_take isl_basic_set *bset);
7558 __isl_give isl_set *isl_basic_set_lexmax(
7559 __isl_take isl_basic_set *bset);
7560 __isl_give isl_set *isl_set_lexmin(
7561 __isl_take isl_set *set);
7562 __isl_give isl_set *isl_set_lexmax(
7563 __isl_take isl_set *set);
7564 __isl_give isl_union_set *isl_union_set_lexmin(
7565 __isl_take isl_union_set *uset);
7566 __isl_give isl_union_set *isl_union_set_lexmax(
7567 __isl_take isl_union_set *uset);
7569 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7570 the following functions
7571 compute a relation that maps each element of C<dom>
7572 to the single lexicographic minimum or maximum
7573 of the elements that are associated to that same
7574 element in C<map> (or C<bmap>).
7575 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7576 that contains the elements in C<dom> that do not map
7577 to any elements in C<map> (or C<bmap>).
7578 In other words, the union of the domain of the result and of C<*empty>
7581 #include <isl/map.h>
7582 __isl_give isl_map *isl_basic_map_partial_lexmax(
7583 __isl_take isl_basic_map *bmap,
7584 __isl_take isl_basic_set *dom,
7585 __isl_give isl_set **empty);
7586 __isl_give isl_map *isl_basic_map_partial_lexmin(
7587 __isl_take isl_basic_map *bmap,
7588 __isl_take isl_basic_set *dom,
7589 __isl_give isl_set **empty);
7590 __isl_give isl_map *isl_map_partial_lexmax(
7591 __isl_take isl_map *map, __isl_take isl_set *dom,
7592 __isl_give isl_set **empty);
7593 __isl_give isl_map *isl_map_partial_lexmin(
7594 __isl_take isl_map *map, __isl_take isl_set *dom,
7595 __isl_give isl_set **empty);
7597 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7598 return a map mapping each element in the domain of
7599 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7600 of all elements associated to that element.
7601 In case of union relations, the optimum is computed per space.
7603 #include <isl/map.h>
7604 __isl_give isl_map *isl_basic_map_lexmin(
7605 __isl_take isl_basic_map *bmap);
7606 __isl_give isl_map *isl_basic_map_lexmax(
7607 __isl_take isl_basic_map *bmap);
7608 __isl_give isl_map *isl_map_lexmin(
7609 __isl_take isl_map *map);
7610 __isl_give isl_map *isl_map_lexmax(
7611 __isl_take isl_map *map);
7612 __isl_give isl_union_map *isl_union_map_lexmin(
7613 __isl_take isl_union_map *umap);
7614 __isl_give isl_union_map *isl_union_map_lexmax(
7615 __isl_take isl_union_map *umap);
7617 The following functions return their result in the form of
7618 a piecewise multi-affine expression,
7619 but are otherwise equivalent to the corresponding functions
7620 returning a basic set or relation.
7622 #include <isl/set.h>
7623 __isl_give isl_pw_multi_aff *
7624 isl_basic_set_partial_lexmin_pw_multi_aff(
7625 __isl_take isl_basic_set *bset,
7626 __isl_take isl_basic_set *dom,
7627 __isl_give isl_set **empty);
7628 __isl_give isl_pw_multi_aff *
7629 isl_basic_set_partial_lexmax_pw_multi_aff(
7630 __isl_take isl_basic_set *bset,
7631 __isl_take isl_basic_set *dom,
7632 __isl_give isl_set **empty);
7633 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7634 __isl_take isl_set *set);
7635 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7636 __isl_take isl_set *set);
7638 #include <isl/map.h>
7639 __isl_give isl_pw_multi_aff *
7640 isl_basic_map_lexmin_pw_multi_aff(
7641 __isl_take isl_basic_map *bmap);
7642 __isl_give isl_pw_multi_aff *
7643 isl_basic_map_partial_lexmin_pw_multi_aff(
7644 __isl_take isl_basic_map *bmap,
7645 __isl_take isl_basic_set *dom,
7646 __isl_give isl_set **empty);
7647 __isl_give isl_pw_multi_aff *
7648 isl_basic_map_partial_lexmax_pw_multi_aff(
7649 __isl_take isl_basic_map *bmap,
7650 __isl_take isl_basic_set *dom,
7651 __isl_give isl_set **empty);
7652 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7653 __isl_take isl_map *map);
7654 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7655 __isl_take isl_map *map);
7657 The following functions return the lexicographic minimum or maximum
7658 on the shared domain of the inputs and the single defined function
7659 on those parts of the domain where only a single function is defined.
7661 #include <isl/aff.h>
7662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7663 __isl_take isl_pw_multi_aff *pma1,
7664 __isl_take isl_pw_multi_aff *pma2);
7665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7666 __isl_take isl_pw_multi_aff *pma1,
7667 __isl_take isl_pw_multi_aff *pma2);
7669 If the input to a lexicographic optimization problem has
7670 multiple constraints with the same coefficients for the optimized
7671 variables, then, by default, this symmetry is exploited by
7672 replacing those constraints by a single constraint with
7673 an abstract bound, which is in turn bounded by the corresponding terms
7674 in the original constraints.
7675 Without this optimization, the solver would typically consider
7676 all possible orderings of those original bounds, resulting in a needless
7677 decomposition of the domain.
7678 However, the optimization can also result in slowdowns since
7679 an extra parameter is introduced that may get used in additional
7681 The following option determines whether symmetry detection is applied
7682 during lexicographic optimization.
7684 #include <isl/options.h>
7685 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7687 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7691 See also \autoref{s:offline}.
7695 =head2 Ternary Operations
7697 #include <isl/aff.h>
7698 __isl_give isl_pw_aff *isl_pw_aff_cond(
7699 __isl_take isl_pw_aff *cond,
7700 __isl_take isl_pw_aff *pwaff_true,
7701 __isl_take isl_pw_aff *pwaff_false);
7703 The function C<isl_pw_aff_cond> performs a conditional operator
7704 and returns an expression that is equal to C<pwaff_true>
7705 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7706 where C<cond> is zero.
7710 Lists are defined over several element types, including
7711 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7712 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7713 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7714 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7715 Here we take lists of C<isl_set>s as an example.
7716 Lists can be created, copied, modified and freed using the following functions.
7718 #include <isl/set.h>
7719 __isl_give isl_set_list *isl_set_list_from_set(
7720 __isl_take isl_set *el);
7721 __isl_give isl_set_list *isl_set_list_alloc(
7722 isl_ctx *ctx, int n);
7723 __isl_give isl_set_list *isl_set_list_copy(
7724 __isl_keep isl_set_list *list);
7725 __isl_give isl_set_list *isl_set_list_insert(
7726 __isl_take isl_set_list *list, unsigned pos,
7727 __isl_take isl_set *el);
7728 __isl_give isl_set_list *isl_set_list_add(
7729 __isl_take isl_set_list *list,
7730 __isl_take isl_set *el);
7731 __isl_give isl_set_list *isl_set_list_drop(
7732 __isl_take isl_set_list *list,
7733 unsigned first, unsigned n);
7734 __isl_give isl_set_list *isl_set_list_set_set(
7735 __isl_take isl_set_list *list, int index,
7736 __isl_take isl_set *set);
7737 __isl_give isl_set_list *isl_set_list_concat(
7738 __isl_take isl_set_list *list1,
7739 __isl_take isl_set_list *list2);
7740 __isl_give isl_set_list *isl_set_list_map(
7741 __isl_take isl_set_list *list,
7742 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7745 __isl_give isl_set_list *isl_set_list_sort(
7746 __isl_take isl_set_list *list,
7747 int (*cmp)(__isl_keep isl_set *a,
7748 __isl_keep isl_set *b, void *user),
7750 __isl_null isl_set_list *isl_set_list_free(
7751 __isl_take isl_set_list *list);
7753 C<isl_set_list_alloc> creates an empty list with an initial capacity
7754 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7755 add elements to a list, increasing its capacity as needed.
7756 C<isl_set_list_from_set> creates a list with a single element.
7758 Lists can be inspected using the following functions.
7760 #include <isl/set.h>
7761 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7762 __isl_give isl_set *isl_set_list_get_set(
7763 __isl_keep isl_set_list *list, int index);
7764 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7765 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7767 isl_stat isl_set_list_foreach_scc(
7768 __isl_keep isl_set_list *list,
7769 isl_bool (*follows)(__isl_keep isl_set *a,
7770 __isl_keep isl_set *b, void *user),
7772 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7775 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7776 strongly connected components of the graph with as vertices the elements
7777 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7778 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7779 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7781 Lists can be printed using
7783 #include <isl/set.h>
7784 __isl_give isl_printer *isl_printer_print_set_list(
7785 __isl_take isl_printer *p,
7786 __isl_keep isl_set_list *list);
7788 =head2 Associative arrays
7790 Associative arrays map isl objects of a specific type to isl objects
7791 of some (other) specific type. They are defined for several pairs
7792 of types, including (C<isl_map>, C<isl_basic_set>),
7793 (C<isl_id>, C<isl_ast_expr>),
7794 (C<isl_id>, C<isl_id>) and
7795 (C<isl_id>, C<isl_pw_aff>).
7796 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7799 Associative arrays can be created, copied and freed using
7800 the following functions.
7802 #include <isl/id_to_ast_expr.h>
7803 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7804 isl_ctx *ctx, int min_size);
7805 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7806 __isl_keep isl_id_to_ast_expr *id2expr);
7807 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7808 __isl_take isl_id_to_ast_expr *id2expr);
7810 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7811 to specify the expected size of the associative array.
7812 The associative array will be grown automatically as needed.
7814 Associative arrays can be inspected using the following functions.
7816 #include <isl/id_to_ast_expr.h>
7817 __isl_give isl_maybe_isl_ast_expr
7818 isl_id_to_ast_expr_try_get(
7819 __isl_keep isl_id_to_ast_expr *id2expr,
7820 __isl_keep isl_id *key);
7821 isl_bool isl_id_to_ast_expr_has(
7822 __isl_keep isl_id_to_ast_expr *id2expr,
7823 __isl_keep isl_id *key);
7824 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7825 __isl_keep isl_id_to_ast_expr *id2expr,
7826 __isl_take isl_id *key);
7827 isl_stat isl_id_to_ast_expr_foreach(
7828 __isl_keep isl_id_to_ast_expr *id2expr,
7829 isl_stat (*fn)(__isl_take isl_id *key,
7830 __isl_take isl_ast_expr *val, void *user),
7833 The function C<isl_id_to_ast_expr_try_get> returns a structure
7834 containing two elements, C<valid> and C<value>.
7835 If there is a value associated to the key, then C<valid>
7836 is set to C<isl_bool_true> and C<value> contains a copy of
7837 the associated value. Otherwise C<value> is C<NULL> and
7838 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7839 on whether some error has occurred or there simply is no associated value.
7840 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7841 in the structure and
7842 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7844 Associative arrays can be modified using the following functions.
7846 #include <isl/id_to_ast_expr.h>
7847 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7848 __isl_take isl_id_to_ast_expr *id2expr,
7849 __isl_take isl_id *key,
7850 __isl_take isl_ast_expr *val);
7851 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7852 __isl_take isl_id_to_ast_expr *id2expr,
7853 __isl_take isl_id *key);
7855 Associative arrays can be printed using the following function.
7857 #include <isl/id_to_ast_expr.h>
7858 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7859 __isl_take isl_printer *p,
7860 __isl_keep isl_id_to_ast_expr *id2expr);
7864 Vectors can be created, copied and freed using the following functions.
7866 #include <isl/vec.h>
7867 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7869 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7871 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7872 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7874 Note that the elements of a vector created by C<isl_vec_alloc>
7875 may have arbitrary values.
7876 A vector created by C<isl_vec_zero> has elements with value zero.
7877 The elements can be changed and inspected using the following functions.
7879 int isl_vec_size(__isl_keep isl_vec *vec);
7880 __isl_give isl_val *isl_vec_get_element_val(
7881 __isl_keep isl_vec *vec, int pos);
7882 __isl_give isl_vec *isl_vec_set_element_si(
7883 __isl_take isl_vec *vec, int pos, int v);
7884 __isl_give isl_vec *isl_vec_set_element_val(
7885 __isl_take isl_vec *vec, int pos,
7886 __isl_take isl_val *v);
7887 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7889 __isl_give isl_vec *isl_vec_set_val(
7890 __isl_take isl_vec *vec, __isl_take isl_val *v);
7891 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7892 __isl_keep isl_vec *vec2, int pos);
7894 C<isl_vec_get_element> will return a negative value if anything went wrong.
7895 In that case, the value of C<*v> is undefined.
7897 The following function can be used to concatenate two vectors.
7899 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7900 __isl_take isl_vec *vec2);
7904 Matrices can be created, copied and freed using the following functions.
7906 #include <isl/mat.h>
7907 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7908 unsigned n_row, unsigned n_col);
7909 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7910 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7912 Note that the elements of a newly created matrix may have arbitrary values.
7913 The elements can be changed and inspected using the following functions.
7915 int isl_mat_rows(__isl_keep isl_mat *mat);
7916 int isl_mat_cols(__isl_keep isl_mat *mat);
7917 __isl_give isl_val *isl_mat_get_element_val(
7918 __isl_keep isl_mat *mat, int row, int col);
7919 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7920 int row, int col, int v);
7921 __isl_give isl_mat *isl_mat_set_element_val(
7922 __isl_take isl_mat *mat, int row, int col,
7923 __isl_take isl_val *v);
7925 The following function computes the rank of a matrix.
7926 The return value may be -1 if some error occurred.
7928 #include <isl/mat.h>
7929 int isl_mat_rank(__isl_keep isl_mat *mat);
7931 The following function can be used to compute the (right) inverse
7932 of a matrix, i.e., a matrix such that the product of the original
7933 and the inverse (in that order) is a multiple of the identity matrix.
7934 The input matrix is assumed to be of full row-rank.
7936 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7938 The following function can be used to compute the (right) kernel
7939 (or null space) of a matrix, i.e., a matrix such that the product of
7940 the original and the kernel (in that order) is the zero matrix.
7942 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7944 The following function computes a basis for the space spanned
7945 by the rows of a matrix.
7947 __isl_give isl_mat *isl_mat_row_basis(
7948 __isl_take isl_mat *mat);
7950 The following function computes rows that extend a basis of C<mat1>
7951 to a basis that also covers C<mat2>.
7953 __isl_give isl_mat *isl_mat_row_basis_extension(
7954 __isl_take isl_mat *mat1,
7955 __isl_take isl_mat *mat2);
7957 The following function checks whether there is no linear dependence
7958 among the combined rows of "mat1" and "mat2" that is not already present
7959 in "mat1" or "mat2" individually.
7960 If "mat1" and "mat2" have linearly independent rows by themselves,
7961 then this means that there is no linear dependence among all rows together.
7963 isl_bool isl_mat_has_linearly_independent_rows(
7964 __isl_keep isl_mat *mat1,
7965 __isl_keep isl_mat *mat2);
7967 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7969 The following functions determine
7970 an upper or lower bound on a quasipolynomial over its domain.
7972 __isl_give isl_pw_qpolynomial_fold *
7973 isl_pw_qpolynomial_bound(
7974 __isl_take isl_pw_qpolynomial *pwqp,
7975 enum isl_fold type, int *tight);
7977 __isl_give isl_union_pw_qpolynomial_fold *
7978 isl_union_pw_qpolynomial_bound(
7979 __isl_take isl_union_pw_qpolynomial *upwqp,
7980 enum isl_fold type, int *tight);
7982 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7983 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7984 is the returned bound is known be tight, i.e., for each value
7985 of the parameters there is at least
7986 one element in the domain that reaches the bound.
7987 If the domain of C<pwqp> is not wrapping, then the bound is computed
7988 over all elements in that domain and the result has a purely parametric
7989 domain. If the domain of C<pwqp> is wrapping, then the bound is
7990 computed over the range of the wrapped relation. The domain of the
7991 wrapped relation becomes the domain of the result.
7993 =head2 Parametric Vertex Enumeration
7995 The parametric vertex enumeration described in this section
7996 is mainly intended to be used internally and by the C<barvinok>
7999 #include <isl/vertices.h>
8000 __isl_give isl_vertices *isl_basic_set_compute_vertices(
8001 __isl_keep isl_basic_set *bset);
8003 The function C<isl_basic_set_compute_vertices> performs the
8004 actual computation of the parametric vertices and the chamber
8005 decomposition and stores the result in an C<isl_vertices> object.
8006 This information can be queried by either iterating over all
8007 the vertices or iterating over all the chambers or cells
8008 and then iterating over all vertices that are active on the chamber.
8010 isl_stat isl_vertices_foreach_vertex(
8011 __isl_keep isl_vertices *vertices,
8012 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8013 void *user), void *user);
8015 isl_stat isl_vertices_foreach_cell(
8016 __isl_keep isl_vertices *vertices,
8017 isl_stat (*fn)(__isl_take isl_cell *cell,
8018 void *user), void *user);
8019 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8020 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8021 void *user), void *user);
8023 Other operations that can be performed on an C<isl_vertices> object are
8026 int isl_vertices_get_n_vertices(
8027 __isl_keep isl_vertices *vertices);
8028 __isl_null isl_vertices *isl_vertices_free(
8029 __isl_take isl_vertices *vertices);
8031 Vertices can be inspected and destroyed using the following functions.
8033 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8034 __isl_give isl_basic_set *isl_vertex_get_domain(
8035 __isl_keep isl_vertex *vertex);
8036 __isl_give isl_multi_aff *isl_vertex_get_expr(
8037 __isl_keep isl_vertex *vertex);
8038 void isl_vertex_free(__isl_take isl_vertex *vertex);
8040 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8041 describing the vertex in terms of the parameters,
8042 while C<isl_vertex_get_domain> returns the activity domain
8045 Chambers can be inspected and destroyed using the following functions.
8047 __isl_give isl_basic_set *isl_cell_get_domain(
8048 __isl_keep isl_cell *cell);
8049 void isl_cell_free(__isl_take isl_cell *cell);
8051 =head1 Polyhedral Compilation Library
8053 This section collects functionality in C<isl> that has been specifically
8054 designed for use during polyhedral compilation.
8056 =head2 Schedule Trees
8058 A schedule tree is a structured representation of a schedule,
8059 assigning a relative order to a set of domain elements.
8060 The relative order expressed by the schedule tree is
8061 defined recursively. In particular, the order between
8062 two domain elements is determined by the node that is closest
8063 to the root that refers to both elements and that orders them apart.
8064 Each node in the tree is of one of several types.
8065 The root node is always of type C<isl_schedule_node_domain>
8066 (or C<isl_schedule_node_extension>)
8067 and it describes the (extra) domain elements to which the schedule applies.
8068 The other types of nodes are as follows.
8072 =item C<isl_schedule_node_band>
8074 A band of schedule dimensions. Each schedule dimension is represented
8075 by a union piecewise quasi-affine expression. If this expression
8076 assigns a different value to two domain elements, while all previous
8077 schedule dimensions in the same band assign them the same value,
8078 then the two domain elements are ordered according to these two
8080 Each expression is required to be total in the domain elements
8081 that reach the band node.
8083 =item C<isl_schedule_node_expansion>
8085 An expansion node maps each of the domain elements that reach the node
8086 to one or more domain elements. The image of this mapping forms
8087 the set of domain elements that reach the child of the expansion node.
8088 The function that maps each of the expanded domain elements
8089 to the original domain element from which it was expanded
8090 is called the contraction.
8092 =item C<isl_schedule_node_filter>
8094 A filter node does not impose any ordering, but rather intersects
8095 the set of domain elements that the current subtree refers to
8096 with a given union set. The subtree of the filter node only
8097 refers to domain elements in the intersection.
8098 A filter node is typically only used as a child of a sequence or
8101 =item C<isl_schedule_node_leaf>
8103 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8105 =item C<isl_schedule_node_mark>
8107 A mark node can be used to attach any kind of information to a subtree
8108 of the schedule tree.
8110 =item C<isl_schedule_node_sequence>
8112 A sequence node has one or more children, each of which is a filter node.
8113 The filters on these filter nodes form a partition of
8114 the domain elements that the current subtree refers to.
8115 If two domain elements appear in distinct filters then the sequence
8116 node orders them according to the child positions of the corresponding
8119 =item C<isl_schedule_node_set>
8121 A set node is similar to a sequence node, except that
8122 it expresses that domain elements appearing in distinct filters
8123 may have any order. The order of the children of a set node
8124 is therefore also immaterial.
8128 The following node types are only supported by the AST generator.
8132 =item C<isl_schedule_node_context>
8134 The context describes constraints on the parameters and
8135 the schedule dimensions of outer
8136 bands that the AST generator may assume to hold. It is also the only
8137 kind of node that may introduce additional parameters.
8138 The space of the context is that of the flat product of the outer
8139 band nodes. In particular, if there are no outer band nodes, then
8140 this space is the unnamed zero-dimensional space.
8141 Since a context node references the outer band nodes, any tree
8142 containing a context node is considered to be anchored.
8144 =item C<isl_schedule_node_extension>
8146 An extension node instructs the AST generator to add additional
8147 domain elements that need to be scheduled.
8148 The additional domain elements are described by the range of
8149 the extension map in terms of the outer schedule dimensions,
8150 i.e., the flat product of the outer band nodes.
8151 Note that domain elements are added whenever the AST generator
8152 reaches the extension node, meaning that there are still some
8153 active domain elements for which an AST needs to be generated.
8154 The conditions under which some domain elements are still active
8155 may however not be completely described by the outer AST nodes
8156 generated at that point.
8157 Since an extension node references the outer band nodes, any tree
8158 containing an extension node is considered to be anchored.
8160 An extension node may also appear as the root of a schedule tree,
8161 when it is intended to be inserted into another tree
8162 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8163 In this case, the domain of the extension node should
8164 correspond to the flat product of the outer band nodes
8165 in this other schedule tree at the point where the extension tree
8168 =item C<isl_schedule_node_guard>
8170 The guard describes constraints on the parameters and
8171 the schedule dimensions of outer
8172 bands that need to be enforced by the outer nodes
8173 in the generated AST.
8174 That is, the part of the AST that is generated from descendants
8175 of the guard node can assume that these constraints are satisfied.
8176 The space of the guard is that of the flat product of the outer
8177 band nodes. In particular, if there are no outer band nodes, then
8178 this space is the unnamed zero-dimensional space.
8179 Since a guard node references the outer band nodes, any tree
8180 containing a guard node is considered to be anchored.
8184 Except for the C<isl_schedule_node_context> nodes,
8185 none of the nodes may introduce any parameters that were not
8186 already present in the root domain node.
8188 A schedule tree is encapsulated in an C<isl_schedule> object.
8189 The simplest such objects, those with a tree consisting of single domain node,
8190 can be created using the following functions with either an empty
8191 domain or a given domain.
8193 #include <isl/schedule.h>
8194 __isl_give isl_schedule *isl_schedule_empty(
8195 __isl_take isl_space *space);
8196 __isl_give isl_schedule *isl_schedule_from_domain(
8197 __isl_take isl_union_set *domain);
8199 The function C<isl_schedule_constraints_compute_schedule> described
8200 in L</"Scheduling"> can also be used to construct schedules.
8202 C<isl_schedule> objects may be copied and freed using the following functions.
8204 #include <isl/schedule.h>
8205 __isl_give isl_schedule *isl_schedule_copy(
8206 __isl_keep isl_schedule *sched);
8207 __isl_null isl_schedule *isl_schedule_free(
8208 __isl_take isl_schedule *sched);
8210 The following functions checks whether two C<isl_schedule> objects
8211 are obviously the same.
8213 #include <isl/schedule.h>
8214 isl_bool isl_schedule_plain_is_equal(
8215 __isl_keep isl_schedule *schedule1,
8216 __isl_keep isl_schedule *schedule2);
8218 The domain of the schedule, i.e., the domain described by the root node,
8219 can be obtained using the following function.
8221 #include <isl/schedule.h>
8222 __isl_give isl_union_set *isl_schedule_get_domain(
8223 __isl_keep isl_schedule *schedule);
8225 An extra top-level band node (right underneath the domain node) can
8226 be introduced into the schedule using the following function.
8227 The schedule tree is assumed not to have any anchored nodes.
8229 #include <isl/schedule.h>
8230 __isl_give isl_schedule *
8231 isl_schedule_insert_partial_schedule(
8232 __isl_take isl_schedule *schedule,
8233 __isl_take isl_multi_union_pw_aff *partial);
8235 A top-level context node (right underneath the domain node) can
8236 be introduced into the schedule using the following function.
8238 #include <isl/schedule.h>
8239 __isl_give isl_schedule *isl_schedule_insert_context(
8240 __isl_take isl_schedule *schedule,
8241 __isl_take isl_set *context)
8243 A top-level guard node (right underneath the domain node) can
8244 be introduced into the schedule using the following function.
8246 #include <isl/schedule.h>
8247 __isl_give isl_schedule *isl_schedule_insert_guard(
8248 __isl_take isl_schedule *schedule,
8249 __isl_take isl_set *guard)
8251 A schedule that combines two schedules either in the given
8252 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8253 or an C<isl_schedule_node_set> node,
8254 can be created using the following functions.
8256 #include <isl/schedule.h>
8257 __isl_give isl_schedule *isl_schedule_sequence(
8258 __isl_take isl_schedule *schedule1,
8259 __isl_take isl_schedule *schedule2);
8260 __isl_give isl_schedule *isl_schedule_set(
8261 __isl_take isl_schedule *schedule1,
8262 __isl_take isl_schedule *schedule2);
8264 The domains of the two input schedules need to be disjoint.
8266 The following function can be used to restrict the domain
8267 of a schedule with a domain node as root to be a subset of the given union set.
8268 This operation may remove nodes in the tree that have become
8271 #include <isl/schedule.h>
8272 __isl_give isl_schedule *isl_schedule_intersect_domain(
8273 __isl_take isl_schedule *schedule,
8274 __isl_take isl_union_set *domain);
8276 The following function can be used to simplify the domain
8277 of a schedule with a domain node as root with respect to the given
8280 #include <isl/schedule.h>
8281 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8282 __isl_take isl_schedule *schedule,
8283 __isl_take isl_set *context);
8285 The following function resets the user pointers on all parameter
8286 and tuple identifiers referenced by the nodes of the given schedule.
8288 #include <isl/schedule.h>
8289 __isl_give isl_schedule *isl_schedule_reset_user(
8290 __isl_take isl_schedule *schedule);
8292 The following function aligns the parameters of all nodes
8293 in the given schedule to the given space.
8295 #include <isl/schedule.h>
8296 __isl_give isl_schedule *isl_schedule_align_params(
8297 __isl_take isl_schedule *schedule,
8298 __isl_take isl_space *space);
8300 The following function allows the user to plug in a given function
8301 in the iteration domains. The input schedule is not allowed to contain
8302 any expansion nodes.
8304 #include <isl/schedule.h>
8305 __isl_give isl_schedule *
8306 isl_schedule_pullback_union_pw_multi_aff(
8307 __isl_take isl_schedule *schedule,
8308 __isl_take isl_union_pw_multi_aff *upma);
8310 The following function can be used to plug in the schedule C<expansion>
8311 in the leaves of C<schedule>, where C<contraction> describes how
8312 the domain elements of C<expansion> map to the domain elements
8313 at the original leaves of C<schedule>.
8314 The resulting schedule will contain expansion nodes, unless
8315 C<contraction> is an identity function.
8317 #include <isl/schedule.h>
8318 __isl_give isl_schedule *isl_schedule_expand(
8319 __isl_take isl_schedule *schedule,
8320 __isl_take isl_union_pw_multi_aff *contraction,
8321 __isl_take isl_schedule *expansion);
8323 An C<isl_union_map> representation of the schedule can be obtained
8324 from an C<isl_schedule> using the following function.
8326 #include <isl/schedule.h>
8327 __isl_give isl_union_map *isl_schedule_get_map(
8328 __isl_keep isl_schedule *sched);
8330 The resulting relation encodes the same relative ordering as
8331 the schedule by mapping the domain elements to a common schedule space.
8332 If the schedule_separate_components option is set, then the order
8333 of the children of a set node is explicitly encoded in the result.
8334 If the tree contains any expansion nodes, then the relation
8335 is formulated in terms of the expanded domain elements.
8337 Schedules can be read from input using the following functions.
8339 #include <isl/schedule.h>
8340 __isl_give isl_schedule *isl_schedule_read_from_file(
8341 isl_ctx *ctx, FILE *input);
8342 __isl_give isl_schedule *isl_schedule_read_from_str(
8343 isl_ctx *ctx, const char *str);
8345 A representation of the schedule can be printed using
8347 #include <isl/schedule.h>
8348 __isl_give isl_printer *isl_printer_print_schedule(
8349 __isl_take isl_printer *p,
8350 __isl_keep isl_schedule *schedule);
8351 __isl_give char *isl_schedule_to_str(
8352 __isl_keep isl_schedule *schedule);
8354 C<isl_schedule_to_str> prints the schedule in flow format.
8356 The schedule tree can be traversed through the use of
8357 C<isl_schedule_node> objects that point to a particular
8358 position in the schedule tree. Whenever a C<isl_schedule_node>
8359 is used to modify a node in the schedule tree, the original schedule
8360 tree is left untouched and the modifications are performed to a copy
8361 of the tree. The returned C<isl_schedule_node> then points to
8362 this modified copy of the tree.
8364 The root of the schedule tree can be obtained using the following function.
8366 #include <isl/schedule.h>
8367 __isl_give isl_schedule_node *isl_schedule_get_root(
8368 __isl_keep isl_schedule *schedule);
8370 A pointer to a newly created schedule tree with a single domain
8371 node can be created using the following functions.
8373 #include <isl/schedule_node.h>
8374 __isl_give isl_schedule_node *
8375 isl_schedule_node_from_domain(
8376 __isl_take isl_union_set *domain);
8377 __isl_give isl_schedule_node *
8378 isl_schedule_node_from_extension(
8379 __isl_take isl_union_map *extension);
8381 C<isl_schedule_node_from_extension> creates a tree with an extension
8384 Schedule nodes can be copied and freed using the following functions.
8386 #include <isl/schedule_node.h>
8387 __isl_give isl_schedule_node *isl_schedule_node_copy(
8388 __isl_keep isl_schedule_node *node);
8389 __isl_null isl_schedule_node *isl_schedule_node_free(
8390 __isl_take isl_schedule_node *node);
8392 The following functions can be used to check if two schedule
8393 nodes point to the same position in the same schedule.
8395 #include <isl/schedule_node.h>
8396 isl_bool isl_schedule_node_is_equal(
8397 __isl_keep isl_schedule_node *node1,
8398 __isl_keep isl_schedule_node *node2);
8400 The following properties can be obtained from a schedule node.
8402 #include <isl/schedule_node.h>
8403 enum isl_schedule_node_type isl_schedule_node_get_type(
8404 __isl_keep isl_schedule_node *node);
8405 enum isl_schedule_node_type
8406 isl_schedule_node_get_parent_type(
8407 __isl_keep isl_schedule_node *node);
8408 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8409 __isl_keep isl_schedule_node *node);
8411 The function C<isl_schedule_node_get_type> returns the type of
8412 the node, while C<isl_schedule_node_get_parent_type> returns
8413 type of the parent of the node, which is required to exist.
8414 The function C<isl_schedule_node_get_schedule> returns a copy
8415 to the schedule to which the node belongs.
8417 The following functions can be used to move the schedule node
8418 to a different position in the tree or to check if such a position
8421 #include <isl/schedule_node.h>
8422 isl_bool isl_schedule_node_has_parent(
8423 __isl_keep isl_schedule_node *node);
8424 __isl_give isl_schedule_node *isl_schedule_node_parent(
8425 __isl_take isl_schedule_node *node);
8426 __isl_give isl_schedule_node *isl_schedule_node_root(
8427 __isl_take isl_schedule_node *node);
8428 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8429 __isl_take isl_schedule_node *node,
8431 int isl_schedule_node_n_children(
8432 __isl_keep isl_schedule_node *node);
8433 __isl_give isl_schedule_node *isl_schedule_node_child(
8434 __isl_take isl_schedule_node *node, int pos);
8435 isl_bool isl_schedule_node_has_children(
8436 __isl_keep isl_schedule_node *node);
8437 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8438 __isl_take isl_schedule_node *node);
8439 isl_bool isl_schedule_node_has_previous_sibling(
8440 __isl_keep isl_schedule_node *node);
8441 __isl_give isl_schedule_node *
8442 isl_schedule_node_previous_sibling(
8443 __isl_take isl_schedule_node *node);
8444 isl_bool isl_schedule_node_has_next_sibling(
8445 __isl_keep isl_schedule_node *node);
8446 __isl_give isl_schedule_node *
8447 isl_schedule_node_next_sibling(
8448 __isl_take isl_schedule_node *node);
8450 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8451 is the node itself, the ancestor of generation 1 is its parent and so on.
8453 It is also possible to query the number of ancestors of a node,
8454 the position of the current node
8455 within the children of its parent, the position of the subtree
8456 containing a node within the children of an ancestor
8457 or to obtain a copy of a given
8458 child without destroying the current node.
8459 Given two nodes that point to the same schedule, their closest
8460 shared ancestor can be obtained using
8461 C<isl_schedule_node_get_shared_ancestor>.
8463 #include <isl/schedule_node.h>
8464 int isl_schedule_node_get_tree_depth(
8465 __isl_keep isl_schedule_node *node);
8466 int isl_schedule_node_get_child_position(
8467 __isl_keep isl_schedule_node *node);
8468 int isl_schedule_node_get_ancestor_child_position(
8469 __isl_keep isl_schedule_node *node,
8470 __isl_keep isl_schedule_node *ancestor);
8471 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8472 __isl_keep isl_schedule_node *node, int pos);
8473 __isl_give isl_schedule_node *
8474 isl_schedule_node_get_shared_ancestor(
8475 __isl_keep isl_schedule_node *node1,
8476 __isl_keep isl_schedule_node *node2);
8478 All nodes in a schedule tree or
8479 all descendants of a specific node (including the node) can be visited
8480 in depth-first pre-order using the following functions.
8482 #include <isl/schedule.h>
8483 isl_stat isl_schedule_foreach_schedule_node_top_down(
8484 __isl_keep isl_schedule *sched,
8485 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8486 void *user), void *user);
8488 #include <isl/schedule_node.h>
8489 isl_stat isl_schedule_node_foreach_descendant_top_down(
8490 __isl_keep isl_schedule_node *node,
8491 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8492 void *user), void *user);
8494 The callback function is slightly different from the usual
8495 callbacks in that it not only indicates success (non-negative result)
8496 or failure (negative result), but also indicates whether the children
8497 of the given node should be visited. In particular, if the callback
8498 returns a positive value, then the children are visited, but if
8499 the callback returns zero, then the children are not visited.
8501 The following functions checks whether
8502 all descendants of a specific node (including the node itself)
8503 satisfy a user-specified test.
8505 #include <isl/schedule_node.h>
8506 isl_bool isl_schedule_node_every_descendant(
8507 __isl_keep isl_schedule_node *node,
8508 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8509 void *user), void *user)
8511 The ancestors of a node in a schedule tree can be visited from
8512 the root down to and including the parent of the node using
8513 the following function.
8515 #include <isl/schedule_node.h>
8516 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8517 __isl_keep isl_schedule_node *node,
8518 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8519 void *user), void *user);
8521 The following functions allows for a depth-first post-order
8522 traversal of the nodes in a schedule tree or
8523 of the descendants of a specific node (including the node
8524 itself), where the user callback is allowed to modify the
8527 #include <isl/schedule.h>
8528 __isl_give isl_schedule *
8529 isl_schedule_map_schedule_node_bottom_up(
8530 __isl_take isl_schedule *schedule,
8531 __isl_give isl_schedule_node *(*fn)(
8532 __isl_take isl_schedule_node *node,
8533 void *user), void *user);
8535 #include <isl/schedule_node.h>
8536 __isl_give isl_schedule_node *
8537 isl_schedule_node_map_descendant_bottom_up(
8538 __isl_take isl_schedule_node *node,
8539 __isl_give isl_schedule_node *(*fn)(
8540 __isl_take isl_schedule_node *node,
8541 void *user), void *user);
8543 The traversal continues from the node returned by the callback function.
8544 It is the responsibility of the user to ensure that this does not
8545 lead to an infinite loop. It is safest to always return a pointer
8546 to the same position (same ancestors and child positions) as the input node.
8548 The following function removes a node (along with its descendants)
8549 from a schedule tree and returns a pointer to the leaf at the
8550 same position in the updated tree.
8551 It is not allowed to remove the root of a schedule tree or
8552 a child of a set or sequence node.
8554 #include <isl/schedule_node.h>
8555 __isl_give isl_schedule_node *isl_schedule_node_cut(
8556 __isl_take isl_schedule_node *node);
8558 The following function removes a single node
8559 from a schedule tree and returns a pointer to the child
8560 of the node, now located at the position of the original node
8561 or to a leaf node at that position if there was no child.
8562 It is not allowed to remove the root of a schedule tree,
8563 a set or sequence node, a child of a set or sequence node or
8564 a band node with an anchored subtree.
8566 #include <isl/schedule_node.h>
8567 __isl_give isl_schedule_node *isl_schedule_node_delete(
8568 __isl_take isl_schedule_node *node);
8570 Most nodes in a schedule tree only contain local information.
8571 In some cases, however, a node may also refer to the schedule dimensions
8572 of its outer band nodes.
8573 This means that the position of the node within the tree should
8574 not be changed, or at least that no changes are performed to the
8575 outer band nodes. The following function can be used to test
8576 whether the subtree rooted at a given node contains any such nodes.
8578 #include <isl/schedule_node.h>
8579 isl_bool isl_schedule_node_is_subtree_anchored(
8580 __isl_keep isl_schedule_node *node);
8582 The following function resets the user pointers on all parameter
8583 and tuple identifiers referenced by the given schedule node.
8585 #include <isl/schedule_node.h>
8586 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8587 __isl_take isl_schedule_node *node);
8589 The following function aligns the parameters of the given schedule
8590 node to the given space.
8592 #include <isl/schedule_node.h>
8593 __isl_give isl_schedule_node *
8594 isl_schedule_node_align_params(
8595 __isl_take isl_schedule_node *node,
8596 __isl_take isl_space *space);
8598 Several node types have their own functions for querying
8599 (and in some cases setting) some node type specific properties.
8601 #include <isl/schedule_node.h>
8602 __isl_give isl_space *isl_schedule_node_band_get_space(
8603 __isl_keep isl_schedule_node *node);
8604 __isl_give isl_multi_union_pw_aff *
8605 isl_schedule_node_band_get_partial_schedule(
8606 __isl_keep isl_schedule_node *node);
8607 __isl_give isl_union_map *
8608 isl_schedule_node_band_get_partial_schedule_union_map(
8609 __isl_keep isl_schedule_node *node);
8610 unsigned isl_schedule_node_band_n_member(
8611 __isl_keep isl_schedule_node *node);
8612 isl_bool isl_schedule_node_band_member_get_coincident(
8613 __isl_keep isl_schedule_node *node, int pos);
8614 __isl_give isl_schedule_node *
8615 isl_schedule_node_band_member_set_coincident(
8616 __isl_take isl_schedule_node *node, int pos,
8618 isl_bool isl_schedule_node_band_get_permutable(
8619 __isl_keep isl_schedule_node *node);
8620 __isl_give isl_schedule_node *
8621 isl_schedule_node_band_set_permutable(
8622 __isl_take isl_schedule_node *node, int permutable);
8623 enum isl_ast_loop_type
8624 isl_schedule_node_band_member_get_ast_loop_type(
8625 __isl_keep isl_schedule_node *node, int pos);
8626 __isl_give isl_schedule_node *
8627 isl_schedule_node_band_member_set_ast_loop_type(
8628 __isl_take isl_schedule_node *node, int pos,
8629 enum isl_ast_loop_type type);
8630 __isl_give isl_union_set *
8631 enum isl_ast_loop_type
8632 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8633 __isl_keep isl_schedule_node *node, int pos);
8634 __isl_give isl_schedule_node *
8635 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8636 __isl_take isl_schedule_node *node, int pos,
8637 enum isl_ast_loop_type type);
8638 isl_schedule_node_band_get_ast_build_options(
8639 __isl_keep isl_schedule_node *node);
8640 __isl_give isl_schedule_node *
8641 isl_schedule_node_band_set_ast_build_options(
8642 __isl_take isl_schedule_node *node,
8643 __isl_take isl_union_set *options);
8644 __isl_give isl_set *
8645 isl_schedule_node_band_get_ast_isolate_option(
8646 __isl_keep isl_schedule_node *node);
8648 The function C<isl_schedule_node_band_get_space> returns the space
8649 of the partial schedule of the band.
8650 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8651 returns a representation of the partial schedule of the band node
8652 in the form of an C<isl_union_map>.
8653 The coincident and permutable properties are set by
8654 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8656 A scheduling dimension is considered to be ``coincident''
8657 if it satisfies the coincidence constraints within its band.
8658 That is, if the dependence distances of the coincidence
8659 constraints are all zero in that direction (for fixed
8660 iterations of outer bands).
8661 A band is marked permutable if it was produced using the Pluto-like scheduler.
8662 Note that the scheduler may have to resort to a Feautrier style scheduling
8663 step even if the default scheduler is used.
8664 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8665 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8666 For the meaning of these loop AST generation types and the difference
8667 between the regular loop AST generation type and the isolate
8668 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8669 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8670 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8671 may return C<isl_ast_loop_error> if an error occurs.
8672 The AST build options govern how an AST is generated for
8673 the individual schedule dimensions during AST generation.
8674 See L</"AST Generation Options (Schedule Tree)">.
8675 The isolate option for the given node can be extracted from these
8676 AST build options using the function
8677 C<isl_schedule_node_band_get_ast_isolate_option>.
8679 #include <isl/schedule_node.h>
8680 __isl_give isl_set *
8681 isl_schedule_node_context_get_context(
8682 __isl_keep isl_schedule_node *node);
8684 #include <isl/schedule_node.h>
8685 __isl_give isl_union_set *
8686 isl_schedule_node_domain_get_domain(
8687 __isl_keep isl_schedule_node *node);
8689 #include <isl/schedule_node.h>
8690 __isl_give isl_union_map *
8691 isl_schedule_node_expansion_get_expansion(
8692 __isl_keep isl_schedule_node *node);
8693 __isl_give isl_union_pw_multi_aff *
8694 isl_schedule_node_expansion_get_contraction(
8695 __isl_keep isl_schedule_node *node);
8697 #include <isl/schedule_node.h>
8698 __isl_give isl_union_map *
8699 isl_schedule_node_extension_get_extension(
8700 __isl_keep isl_schedule_node *node);
8702 #include <isl/schedule_node.h>
8703 __isl_give isl_union_set *
8704 isl_schedule_node_filter_get_filter(
8705 __isl_keep isl_schedule_node *node);
8707 #include <isl/schedule_node.h>
8708 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8709 __isl_keep isl_schedule_node *node);
8711 #include <isl/schedule_node.h>
8712 __isl_give isl_id *isl_schedule_node_mark_get_id(
8713 __isl_keep isl_schedule_node *node);
8715 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8716 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8717 partial schedules related to the node.
8719 #include <isl/schedule_node.h>
8720 __isl_give isl_multi_union_pw_aff *
8721 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8722 __isl_keep isl_schedule_node *node);
8723 __isl_give isl_union_pw_multi_aff *
8724 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8725 __isl_keep isl_schedule_node *node);
8726 __isl_give isl_union_map *
8727 isl_schedule_node_get_prefix_schedule_union_map(
8728 __isl_keep isl_schedule_node *node);
8729 __isl_give isl_union_map *
8730 isl_schedule_node_get_prefix_schedule_relation(
8731 __isl_keep isl_schedule_node *node);
8732 __isl_give isl_union_map *
8733 isl_schedule_node_get_subtree_schedule_union_map(
8734 __isl_keep isl_schedule_node *node);
8736 In particular, the functions
8737 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8738 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8739 and C<isl_schedule_node_get_prefix_schedule_union_map>
8740 return a relative ordering on the domain elements that reach the given
8741 node determined by its ancestors.
8742 The function C<isl_schedule_node_get_prefix_schedule_relation>
8743 additionally includes the domain constraints in the result.
8744 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8745 returns a representation of the partial schedule defined by the
8746 subtree rooted at the given node.
8747 If the tree contains any expansion nodes, then the subtree schedule
8748 is formulated in terms of the expanded domain elements.
8749 The tree passed to functions returning a prefix schedule
8750 may only contain extension nodes if these would not affect
8751 the result of these functions. That is, if one of the ancestors
8752 is an extension node, then all of the domain elements that were
8753 added by the extension node need to have been filtered out
8754 by filter nodes between the extension node and the input node.
8755 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8756 may not contain in extension nodes in the selected subtree.
8758 The expansion/contraction defined by an entire subtree, combining
8759 the expansions/contractions
8760 on the expansion nodes in the subtree, can be obtained using
8761 the following functions.
8763 #include <isl/schedule_node.h>
8764 __isl_give isl_union_map *
8765 isl_schedule_node_get_subtree_expansion(
8766 __isl_keep isl_schedule_node *node);
8767 __isl_give isl_union_pw_multi_aff *
8768 isl_schedule_node_get_subtree_contraction(
8769 __isl_keep isl_schedule_node *node);
8771 The total number of outer band members of given node, i.e.,
8772 the shared output dimension of the maps in the result
8773 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8774 using the following function.
8776 #include <isl/schedule_node.h>
8777 int isl_schedule_node_get_schedule_depth(
8778 __isl_keep isl_schedule_node *node);
8780 The following functions return the elements that reach the given node
8781 or the union of universes in the spaces that contain these elements.
8783 #include <isl/schedule_node.h>
8784 __isl_give isl_union_set *
8785 isl_schedule_node_get_domain(
8786 __isl_keep isl_schedule_node *node);
8787 __isl_give isl_union_set *
8788 isl_schedule_node_get_universe_domain(
8789 __isl_keep isl_schedule_node *node);
8791 The input tree of C<isl_schedule_node_get_domain>
8792 may only contain extension nodes if these would not affect
8793 the result of this function. That is, if one of the ancestors
8794 is an extension node, then all of the domain elements that were
8795 added by the extension node need to have been filtered out
8796 by filter nodes between the extension node and the input node.
8798 The following functions can be used to introduce additional nodes
8799 in the schedule tree. The new node is introduced at the point
8800 in the tree where the C<isl_schedule_node> points to and
8801 the results points to the new node.
8803 #include <isl/schedule_node.h>
8804 __isl_give isl_schedule_node *
8805 isl_schedule_node_insert_partial_schedule(
8806 __isl_take isl_schedule_node *node,
8807 __isl_take isl_multi_union_pw_aff *schedule);
8809 This function inserts a new band node with (the greatest integer
8810 part of) the given partial schedule.
8811 The subtree rooted at the given node is assumed not to have
8814 #include <isl/schedule_node.h>
8815 __isl_give isl_schedule_node *
8816 isl_schedule_node_insert_context(
8817 __isl_take isl_schedule_node *node,
8818 __isl_take isl_set *context);
8820 This function inserts a new context node with the given context constraints.
8822 #include <isl/schedule_node.h>
8823 __isl_give isl_schedule_node *
8824 isl_schedule_node_insert_filter(
8825 __isl_take isl_schedule_node *node,
8826 __isl_take isl_union_set *filter);
8828 This function inserts a new filter node with the given filter.
8829 If the original node already pointed to a filter node, then the
8830 two filter nodes are merged into one.
8832 #include <isl/schedule_node.h>
8833 __isl_give isl_schedule_node *
8834 isl_schedule_node_insert_guard(
8835 __isl_take isl_schedule_node *node,
8836 __isl_take isl_set *guard);
8838 This function inserts a new guard node with the given guard constraints.
8840 #include <isl/schedule_node.h>
8841 __isl_give isl_schedule_node *
8842 isl_schedule_node_insert_mark(
8843 __isl_take isl_schedule_node *node,
8844 __isl_take isl_id *mark);
8846 This function inserts a new mark node with the give mark identifier.
8848 #include <isl/schedule_node.h>
8849 __isl_give isl_schedule_node *
8850 isl_schedule_node_insert_sequence(
8851 __isl_take isl_schedule_node *node,
8852 __isl_take isl_union_set_list *filters);
8853 __isl_give isl_schedule_node *
8854 isl_schedule_node_insert_set(
8855 __isl_take isl_schedule_node *node,
8856 __isl_take isl_union_set_list *filters);
8858 These functions insert a new sequence or set node with the given
8859 filters as children.
8861 #include <isl/schedule_node.h>
8862 __isl_give isl_schedule_node *isl_schedule_node_group(
8863 __isl_take isl_schedule_node *node,
8864 __isl_take isl_id *group_id);
8866 This function introduces an expansion node in between the current
8867 node and its parent that expands instances of a space with tuple
8868 identifier C<group_id> to the original domain elements that reach
8869 the node. The group instances are identified by the prefix schedule
8870 of those domain elements. The ancestors of the node are adjusted
8871 to refer to the group instances instead of the original domain
8872 elements. The return value points to the same node in the updated
8873 schedule tree as the input node, i.e., to the child of the newly
8874 introduced expansion node. Grouping instances of different statements
8875 ensures that they will be treated as a single statement by the
8876 AST generator up to the point of the expansion node.
8878 The following function can be used to flatten a nested
8881 #include <isl/schedule_node.h>
8882 __isl_give isl_schedule_node *
8883 isl_schedule_node_sequence_splice_child(
8884 __isl_take isl_schedule_node *node, int pos);
8886 That is, given a sequence node C<node> that has another sequence node
8887 in its child at position C<pos> (in particular, the child of that filter
8888 node is a sequence node), attach the children of that other sequence
8889 node as children of C<node>, replacing the original child at position
8892 The partial schedule of a band node can be scaled (down) or reduced using
8893 the following functions.
8895 #include <isl/schedule_node.h>
8896 __isl_give isl_schedule_node *
8897 isl_schedule_node_band_scale(
8898 __isl_take isl_schedule_node *node,
8899 __isl_take isl_multi_val *mv);
8900 __isl_give isl_schedule_node *
8901 isl_schedule_node_band_scale_down(
8902 __isl_take isl_schedule_node *node,
8903 __isl_take isl_multi_val *mv);
8904 __isl_give isl_schedule_node *
8905 isl_schedule_node_band_mod(
8906 __isl_take isl_schedule_node *node,
8907 __isl_take isl_multi_val *mv);
8909 The spaces of the two arguments need to match.
8910 After scaling, the partial schedule is replaced by its greatest
8911 integer part to ensure that the schedule remains integral.
8913 The partial schedule of a band node can be shifted by an
8914 C<isl_multi_union_pw_aff> with a domain that is a superset
8915 of the domain of the partial schedule using
8916 the following function.
8918 #include <isl/schedule_node.h>
8919 __isl_give isl_schedule_node *
8920 isl_schedule_node_band_shift(
8921 __isl_take isl_schedule_node *node,
8922 __isl_take isl_multi_union_pw_aff *shift);
8924 A band node can be tiled using the following function.
8926 #include <isl/schedule_node.h>
8927 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8928 __isl_take isl_schedule_node *node,
8929 __isl_take isl_multi_val *sizes);
8931 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8933 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8934 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8936 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8938 The C<isl_schedule_node_band_tile> function tiles
8939 the band using the given tile sizes inside its schedule.
8940 A new child band node is created to represent the point loops and it is
8941 inserted between the modified band and its children.
8942 The subtree rooted at the given node is assumed not to have
8944 The C<tile_scale_tile_loops> option specifies whether the tile
8945 loops iterators should be scaled by the tile sizes.
8946 If the C<tile_shift_point_loops> option is set, then the point loops
8947 are shifted to start at zero.
8949 A band node can be split into two nested band nodes
8950 using the following function.
8952 #include <isl/schedule_node.h>
8953 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8954 __isl_take isl_schedule_node *node, int pos);
8956 The resulting outer band node contains the first C<pos> dimensions of
8957 the schedule of C<node> while the inner band contains the remaining dimensions.
8958 The schedules of the two band nodes live in anonymous spaces.
8959 The loop AST generation type options and the isolate option
8960 are split over the two band nodes.
8962 A band node can be moved down to the leaves of the subtree rooted
8963 at the band node using the following function.
8965 #include <isl/schedule_node.h>
8966 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8967 __isl_take isl_schedule_node *node);
8969 The subtree rooted at the given node is assumed not to have
8971 The result points to the node in the resulting tree that is in the same
8972 position as the node pointed to by C<node> in the original tree.
8974 #include <isl/schedule_node.h>
8975 __isl_give isl_schedule_node *
8976 isl_schedule_node_order_before(
8977 __isl_take isl_schedule_node *node,
8978 __isl_take isl_union_set *filter);
8979 __isl_give isl_schedule_node *
8980 isl_schedule_node_order_after(
8981 __isl_take isl_schedule_node *node,
8982 __isl_take isl_union_set *filter);
8984 These functions split the domain elements that reach C<node>
8985 into those that satisfy C<filter> and those that do not and
8986 arranges for the elements that do satisfy the filter to be
8987 executed before (in case of C<isl_schedule_node_order_before>)
8988 or after (in case of C<isl_schedule_node_order_after>)
8989 those that do not. The order is imposed by
8990 a sequence node, possibly reusing the grandparent of C<node>
8991 on two copies of the subtree attached to the original C<node>.
8992 Both copies are simplified with respect to their filter.
8994 Return a pointer to the copy of the subtree that does not
8995 satisfy C<filter>. If there is no such copy (because all
8996 reaching domain elements satisfy the filter), then return
8997 the original pointer.
8999 #include <isl/schedule_node.h>
9000 __isl_give isl_schedule_node *
9001 isl_schedule_node_graft_before(
9002 __isl_take isl_schedule_node *node,
9003 __isl_take isl_schedule_node *graft);
9004 __isl_give isl_schedule_node *
9005 isl_schedule_node_graft_after(
9006 __isl_take isl_schedule_node *node,
9007 __isl_take isl_schedule_node *graft);
9009 This function inserts the C<graft> tree into the tree containing C<node>
9010 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9011 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9012 The root node of C<graft>
9013 should be an extension node where the domain of the extension
9014 is the flat product of all outer band nodes of C<node>.
9015 The root node may also be a domain node.
9016 The elements of the domain or the range of the extension may not
9017 intersect with the domain elements that reach "node".
9018 The schedule tree of C<graft> may not be anchored.
9020 The schedule tree of C<node> is modified to include an extension node
9021 corresponding to the root node of C<graft> as a child of the original
9022 parent of C<node>. The original node that C<node> points to and the
9023 child of the root node of C<graft> are attached to this extension node
9024 through a sequence, with appropriate filters and with the child
9025 of C<graft> appearing before or after the original C<node>.
9027 If C<node> already appears inside a sequence that is the child of
9028 an extension node and if the spaces of the new domain elements
9029 do not overlap with those of the original domain elements,
9030 then that extension node is extended with the new extension
9031 rather than introducing a new segment of extension and sequence nodes.
9033 Return a pointer to the same node in the modified tree that
9034 C<node> pointed to in the original tree.
9036 A representation of the schedule node can be printed using
9038 #include <isl/schedule_node.h>
9039 __isl_give isl_printer *isl_printer_print_schedule_node(
9040 __isl_take isl_printer *p,
9041 __isl_keep isl_schedule_node *node);
9042 __isl_give char *isl_schedule_node_to_str(
9043 __isl_keep isl_schedule_node *node);
9045 C<isl_schedule_node_to_str> prints the schedule node in block format.
9047 =head2 Dependence Analysis
9049 C<isl> contains specialized functionality for performing
9050 array dataflow analysis. That is, given a I<sink> access relation,
9051 a collection of possible I<source> accesses and
9052 a collection of I<kill> accesses,
9053 C<isl> can compute relations that describe
9054 for each iteration of the sink access, which iterations
9055 of which of the source access relations may have
9056 accessed the same data element before the given iteration
9057 of the sink access without any intermediate kill of that data element.
9058 The resulting dependence relations map source iterations
9059 to either the corresponding sink iterations or
9060 pairs of corresponding sink iterations and accessed data elements.
9061 To compute standard flow dependences, the sink should be
9062 a read, while the sources should be writes.
9063 If no kills are specified,
9064 then memory based dependence analysis is performed.
9065 If, on the other hand, all sources are also kills,
9066 then value based dependence analysis is performed.
9067 If any of the source accesses are marked as being I<must>
9068 accesses, then they are also treated as kills.
9069 Furthermore, the specification of must-sources results
9070 in the computation of must-dependences.
9071 Only dependences originating in a must access not coscheduled
9072 with any other access to the same element and without
9073 any may accesses between the must access and the sink access
9074 are considered to be must dependences.
9076 =head3 High-level Interface
9078 A high-level interface to dependence analysis is provided
9079 by the following function.
9081 #include <isl/flow.h>
9082 __isl_give isl_union_flow *
9083 isl_union_access_info_compute_flow(
9084 __isl_take isl_union_access_info *access);
9086 The input C<isl_union_access_info> object describes the sink
9087 access relations, the source access relations and a schedule,
9088 while the output C<isl_union_flow> object describes
9089 the resulting dependence relations and the subsets of the
9090 sink relations for which no source was found.
9092 An C<isl_union_access_info> is created, modified, copied and freed using
9093 the following functions.
9095 #include <isl/flow.h>
9096 __isl_give isl_union_access_info *
9097 isl_union_access_info_from_sink(
9098 __isl_take isl_union_map *sink);
9099 __isl_give isl_union_access_info *
9100 isl_union_access_info_set_kill(
9101 __isl_take isl_union_access_info *access,
9102 __isl_take isl_union_map *kill);
9103 __isl_give isl_union_access_info *
9104 isl_union_access_info_set_may_source(
9105 __isl_take isl_union_access_info *access,
9106 __isl_take isl_union_map *may_source);
9107 __isl_give isl_union_access_info *
9108 isl_union_access_info_set_must_source(
9109 __isl_take isl_union_access_info *access,
9110 __isl_take isl_union_map *must_source);
9111 __isl_give isl_union_access_info *
9112 isl_union_access_info_set_schedule(
9113 __isl_take isl_union_access_info *access,
9114 __isl_take isl_schedule *schedule);
9115 __isl_give isl_union_access_info *
9116 isl_union_access_info_set_schedule_map(
9117 __isl_take isl_union_access_info *access,
9118 __isl_take isl_union_map *schedule_map);
9119 __isl_give isl_union_access_info *
9120 isl_union_access_info_copy(
9121 __isl_keep isl_union_access_info *access);
9122 __isl_null isl_union_access_info *
9123 isl_union_access_info_free(
9124 __isl_take isl_union_access_info *access);
9126 The may sources set by C<isl_union_access_info_set_may_source>
9127 do not need to include the must sources set by
9128 C<isl_union_access_info_set_must_source> as a subset.
9129 The kills set by C<isl_union_access_info_set_kill> may overlap
9130 with the may-sources and/or must-sources.
9131 The user is free not to call one (or more) of these functions,
9132 in which case the corresponding set is kept to its empty default.
9133 Similarly, the default schedule initialized by
9134 C<isl_union_access_info_from_sink> is empty.
9135 The current schedule is determined by the last call to either
9136 C<isl_union_access_info_set_schedule> or
9137 C<isl_union_access_info_set_schedule_map>.
9138 The domain of the schedule corresponds to the domains of
9139 the access relations. In particular, the domains of the access
9140 relations are effectively intersected with the domain of the schedule
9141 and only the resulting accesses are considered by the dependence analysis.
9143 An C<isl_union_access_info> object can be read from input
9144 using the following function.
9146 #include <isl/flow.h>
9147 __isl_give isl_union_access_info *
9148 isl_union_access_info_read_from_file(isl_ctx *ctx,
9151 A representation of the information contained in an object
9152 of type C<isl_union_access_info> can be obtained using
9154 #include <isl/flow.h>
9155 __isl_give isl_printer *
9156 isl_printer_print_union_access_info(
9157 __isl_take isl_printer *p,
9158 __isl_keep isl_union_access_info *access);
9159 __isl_give char *isl_union_access_info_to_str(
9160 __isl_keep isl_union_access_info *access);
9162 C<isl_union_access_info_to_str> prints the information in flow format.
9164 The output of C<isl_union_access_info_compute_flow> can be examined,
9165 copied, and freed using the following functions.
9167 #include <isl/flow.h>
9168 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9169 __isl_keep isl_union_flow *flow);
9170 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9171 __isl_keep isl_union_flow *flow);
9172 __isl_give isl_union_map *
9173 isl_union_flow_get_full_must_dependence(
9174 __isl_keep isl_union_flow *flow);
9175 __isl_give isl_union_map *
9176 isl_union_flow_get_full_may_dependence(
9177 __isl_keep isl_union_flow *flow);
9178 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9179 __isl_keep isl_union_flow *flow);
9180 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9181 __isl_keep isl_union_flow *flow);
9182 __isl_give isl_union_flow *isl_union_flow_copy(
9183 __isl_keep isl_union_flow *flow);
9184 __isl_null isl_union_flow *isl_union_flow_free(
9185 __isl_take isl_union_flow *flow);
9187 The relation returned by C<isl_union_flow_get_must_dependence>
9188 relates domain elements of must sources to domain elements of the sink.
9189 The relation returned by C<isl_union_flow_get_may_dependence>
9190 relates domain elements of must or may sources to domain elements of the sink
9191 and includes the previous relation as a subset.
9192 The relation returned by C<isl_union_flow_get_full_must_dependence>
9193 relates domain elements of must sources to pairs of domain elements of the sink
9194 and accessed data elements.
9195 The relation returned by C<isl_union_flow_get_full_may_dependence>
9196 relates domain elements of must or may sources to pairs of
9197 domain elements of the sink and accessed data elements.
9198 This relation includes the previous relation as a subset.
9199 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9200 of the sink relation for which no dependences have been found.
9201 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9202 of the sink relation for which no definite dependences have been found.
9203 That is, it contains those sink access that do not contribute to any
9204 of the elements in the relation returned
9205 by C<isl_union_flow_get_must_dependence>.
9207 A representation of the information contained in an object
9208 of type C<isl_union_flow> can be obtained using
9210 #include <isl/flow.h>
9211 __isl_give isl_printer *isl_printer_print_union_flow(
9212 __isl_take isl_printer *p,
9213 __isl_keep isl_union_flow *flow);
9214 __isl_give char *isl_union_flow_to_str(
9215 __isl_keep isl_union_flow *flow);
9217 C<isl_union_flow_to_str> prints the information in flow format.
9219 =head3 Low-level Interface
9221 A lower-level interface is provided by the following functions.
9223 #include <isl/flow.h>
9225 typedef int (*isl_access_level_before)(void *first, void *second);
9227 __isl_give isl_access_info *isl_access_info_alloc(
9228 __isl_take isl_map *sink,
9229 void *sink_user, isl_access_level_before fn,
9231 __isl_give isl_access_info *isl_access_info_add_source(
9232 __isl_take isl_access_info *acc,
9233 __isl_take isl_map *source, int must,
9235 __isl_null isl_access_info *isl_access_info_free(
9236 __isl_take isl_access_info *acc);
9238 __isl_give isl_flow *isl_access_info_compute_flow(
9239 __isl_take isl_access_info *acc);
9241 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9242 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9243 void *dep_user, void *user),
9245 __isl_give isl_map *isl_flow_get_no_source(
9246 __isl_keep isl_flow *deps, int must);
9247 void isl_flow_free(__isl_take isl_flow *deps);
9249 The function C<isl_access_info_compute_flow> performs the actual
9250 dependence analysis. The other functions are used to construct
9251 the input for this function or to read off the output.
9253 The input is collected in an C<isl_access_info>, which can
9254 be created through a call to C<isl_access_info_alloc>.
9255 The arguments to this functions are the sink access relation
9256 C<sink>, a token C<sink_user> used to identify the sink
9257 access to the user, a callback function for specifying the
9258 relative order of source and sink accesses, and the number
9259 of source access relations that will be added.
9261 The callback function has type C<int (*)(void *first, void *second)>.
9262 The function is called with two user supplied tokens identifying
9263 either a source or the sink and it should return the shared nesting
9264 level and the relative order of the two accesses.
9265 In particular, let I<n> be the number of loops shared by
9266 the two accesses. If C<first> precedes C<second> textually,
9267 then the function should return I<2 * n + 1>; otherwise,
9268 it should return I<2 * n>.
9269 The low-level interface assumes that no sources are coscheduled.
9270 If the information returned by the callback does not allow
9271 the relative order to be determined, then one of the sources
9272 is arbitrarily taken to be executed after the other(s).
9274 The sources can be added to the C<isl_access_info> object by performing
9275 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9276 C<must> indicates whether the source is a I<must> access
9277 or a I<may> access. Note that a multi-valued access relation
9278 should only be marked I<must> if every iteration in the domain
9279 of the relation accesses I<all> elements in its image.
9280 The C<source_user> token is again used to identify
9281 the source access. The range of the source access relation
9282 C<source> should have the same dimension as the range
9283 of the sink access relation.
9284 The C<isl_access_info_free> function should usually not be
9285 called explicitly, because it is already called implicitly by
9286 C<isl_access_info_compute_flow>.
9288 The result of the dependence analysis is collected in an
9289 C<isl_flow>. There may be elements of
9290 the sink access for which no preceding source access could be
9291 found or for which all preceding sources are I<may> accesses.
9292 The relations containing these elements can be obtained through
9293 calls to C<isl_flow_get_no_source>, the first with C<must> set
9294 and the second with C<must> unset.
9295 In the case of standard flow dependence analysis,
9296 with the sink a read and the sources I<must> writes,
9297 the first relation corresponds to the reads from uninitialized
9298 array elements and the second relation is empty.
9299 The actual flow dependences can be extracted using
9300 C<isl_flow_foreach>. This function will call the user-specified
9301 callback function C<fn> for each B<non-empty> dependence between
9302 a source and the sink. The callback function is called
9303 with four arguments, the actual flow dependence relation
9304 mapping source iterations to sink iterations, a boolean that
9305 indicates whether it is a I<must> or I<may> dependence, a token
9306 identifying the source and an additional C<void *> with value
9307 equal to the third argument of the C<isl_flow_foreach> call.
9308 A dependence is marked I<must> if it originates from a I<must>
9309 source and if it is not followed by any I<may> sources.
9311 After finishing with an C<isl_flow>, the user should call
9312 C<isl_flow_free> to free all associated memory.
9314 =head3 Interaction with the Low-level Interface
9316 During the dependence analysis, we frequently need to perform
9317 the following operation. Given a relation between sink iterations
9318 and potential source iterations from a particular source domain,
9319 what is the last potential source iteration corresponding to each
9320 sink iteration. It can sometimes be convenient to adjust
9321 the set of potential source iterations before or after each such operation.
9322 The prototypical example is fuzzy array dataflow analysis,
9323 where we need to analyze if, based on data-dependent constraints,
9324 the sink iteration can ever be executed without one or more of
9325 the corresponding potential source iterations being executed.
9326 If so, we can introduce extra parameters and select an unknown
9327 but fixed source iteration from the potential source iterations.
9328 To be able to perform such manipulations, C<isl> provides the following
9331 #include <isl/flow.h>
9333 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9334 __isl_keep isl_map *source_map,
9335 __isl_keep isl_set *sink, void *source_user,
9337 __isl_give isl_access_info *isl_access_info_set_restrict(
9338 __isl_take isl_access_info *acc,
9339 isl_access_restrict fn, void *user);
9341 The function C<isl_access_info_set_restrict> should be called
9342 before calling C<isl_access_info_compute_flow> and registers a callback function
9343 that will be called any time C<isl> is about to compute the last
9344 potential source. The first argument is the (reverse) proto-dependence,
9345 mapping sink iterations to potential source iterations.
9346 The second argument represents the sink iterations for which
9347 we want to compute the last source iteration.
9348 The third argument is the token corresponding to the source
9349 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9350 The callback is expected to return a restriction on either the input or
9351 the output of the operation computing the last potential source.
9352 If the input needs to be restricted then restrictions are needed
9353 for both the source and the sink iterations. The sink iterations
9354 and the potential source iterations will be intersected with these sets.
9355 If the output needs to be restricted then only a restriction on the source
9356 iterations is required.
9357 If any error occurs, the callback should return C<NULL>.
9358 An C<isl_restriction> object can be created, freed and inspected
9359 using the following functions.
9361 #include <isl/flow.h>
9363 __isl_give isl_restriction *isl_restriction_input(
9364 __isl_take isl_set *source_restr,
9365 __isl_take isl_set *sink_restr);
9366 __isl_give isl_restriction *isl_restriction_output(
9367 __isl_take isl_set *source_restr);
9368 __isl_give isl_restriction *isl_restriction_none(
9369 __isl_take isl_map *source_map);
9370 __isl_give isl_restriction *isl_restriction_empty(
9371 __isl_take isl_map *source_map);
9372 __isl_null isl_restriction *isl_restriction_free(
9373 __isl_take isl_restriction *restr);
9375 C<isl_restriction_none> and C<isl_restriction_empty> are special
9376 cases of C<isl_restriction_input>. C<isl_restriction_none>
9377 is essentially equivalent to
9379 isl_restriction_input(isl_set_universe(
9380 isl_space_range(isl_map_get_space(source_map))),
9382 isl_space_domain(isl_map_get_space(source_map))));
9384 whereas C<isl_restriction_empty> is essentially equivalent to
9386 isl_restriction_input(isl_set_empty(
9387 isl_space_range(isl_map_get_space(source_map))),
9389 isl_space_domain(isl_map_get_space(source_map))));
9393 #include <isl/schedule.h>
9394 __isl_give isl_schedule *
9395 isl_schedule_constraints_compute_schedule(
9396 __isl_take isl_schedule_constraints *sc);
9398 The function C<isl_schedule_constraints_compute_schedule> can be
9399 used to compute a schedule that satisfies the given schedule constraints.
9400 These schedule constraints include the iteration domain for which
9401 a schedule should be computed and dependences between pairs of
9402 iterations. In particular, these dependences include
9403 I<validity> dependences and I<proximity> dependences.
9404 By default, the algorithm used to construct the schedule is similar
9405 to that of C<Pluto>.
9406 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9408 The generated schedule respects all validity dependences.
9409 That is, all dependence distances over these dependences in the
9410 scheduled space are lexicographically positive.
9412 The default algorithm tries to ensure that the dependence distances
9413 over coincidence constraints are zero and to minimize the
9414 dependence distances over proximity dependences.
9415 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9416 for groups of domains where the dependence distances over validity
9417 dependences have only non-negative values.
9418 Note that when minimizing the maximal dependence distance
9419 over proximity dependences, a single affine expression in the parameters
9420 is constructed that bounds all dependence distances. If no such expression
9421 exists, then the algorithm will fail and resort to an alternative
9422 scheduling algorithm. In particular, this means that adding proximity
9423 dependences may eliminate valid solutions. A typical example where this
9424 phenomenon may occur is when some subset of the proximity dependences
9425 has no restriction on some parameter, forcing the coefficient of that
9426 parameter to be zero, while some other subset forces the dependence
9427 distance to depend on that parameter, requiring the same coefficient
9429 When using Feautrier's algorithm, the coincidence and proximity constraints
9430 are only taken into account during the extension to a
9431 full-dimensional schedule.
9433 An C<isl_schedule_constraints> object can be constructed
9434 and manipulated using the following functions.
9436 #include <isl/schedule.h>
9437 __isl_give isl_schedule_constraints *
9438 isl_schedule_constraints_copy(
9439 __isl_keep isl_schedule_constraints *sc);
9440 __isl_give isl_schedule_constraints *
9441 isl_schedule_constraints_on_domain(
9442 __isl_take isl_union_set *domain);
9443 __isl_give isl_schedule_constraints *
9444 isl_schedule_constraints_set_context(
9445 __isl_take isl_schedule_constraints *sc,
9446 __isl_take isl_set *context);
9447 __isl_give isl_schedule_constraints *
9448 isl_schedule_constraints_set_validity(
9449 __isl_take isl_schedule_constraints *sc,
9450 __isl_take isl_union_map *validity);
9451 __isl_give isl_schedule_constraints *
9452 isl_schedule_constraints_set_coincidence(
9453 __isl_take isl_schedule_constraints *sc,
9454 __isl_take isl_union_map *coincidence);
9455 __isl_give isl_schedule_constraints *
9456 isl_schedule_constraints_set_proximity(
9457 __isl_take isl_schedule_constraints *sc,
9458 __isl_take isl_union_map *proximity);
9459 __isl_give isl_schedule_constraints *
9460 isl_schedule_constraints_set_conditional_validity(
9461 __isl_take isl_schedule_constraints *sc,
9462 __isl_take isl_union_map *condition,
9463 __isl_take isl_union_map *validity);
9464 __isl_give isl_schedule_constraints *
9465 isl_schedule_constraints_apply(
9466 __isl_take isl_schedule_constraints *sc,
9467 __isl_take isl_union_map *umap);
9468 __isl_null isl_schedule_constraints *
9469 isl_schedule_constraints_free(
9470 __isl_take isl_schedule_constraints *sc);
9472 The initial C<isl_schedule_constraints> object created by
9473 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9474 That is, it has an empty set of dependences.
9475 The function C<isl_schedule_constraints_set_context> allows the user
9476 to specify additional constraints on the parameters that may
9477 be assumed to hold during the construction of the schedule.
9478 The function C<isl_schedule_constraints_set_validity> replaces the
9479 validity dependences, mapping domain elements I<i> to domain
9480 elements that should be scheduled after I<i>.
9481 The function C<isl_schedule_constraints_set_coincidence> replaces the
9482 coincidence dependences, mapping domain elements I<i> to domain
9483 elements that should be scheduled together with I<I>, if possible.
9484 The function C<isl_schedule_constraints_set_proximity> replaces the
9485 proximity dependences, mapping domain elements I<i> to domain
9486 elements that should be scheduled either before I<I>
9487 or as early as possible after I<i>.
9489 The function C<isl_schedule_constraints_set_conditional_validity>
9490 replaces the conditional validity constraints.
9491 A conditional validity constraint is only imposed when any of the corresponding
9492 conditions is satisfied, i.e., when any of them is non-zero.
9493 That is, the scheduler ensures that within each band if the dependence
9494 distances over the condition constraints are not all zero
9495 then all corresponding conditional validity constraints are respected.
9496 A conditional validity constraint corresponds to a condition
9497 if the two are adjacent, i.e., if the domain of one relation intersect
9498 the range of the other relation.
9499 The typical use case of conditional validity constraints is
9500 to allow order constraints between live ranges to be violated
9501 as long as the live ranges themselves are local to the band.
9502 To allow more fine-grained control over which conditions correspond
9503 to which conditional validity constraints, the domains and ranges
9504 of these relations may include I<tags>. That is, the domains and
9505 ranges of those relation may themselves be wrapped relations
9506 where the iteration domain appears in the domain of those wrapped relations
9507 and the range of the wrapped relations can be arbitrarily chosen
9508 by the user. Conditions and conditional validity constraints are only
9509 considered adjacent to each other if the entire wrapped relation matches.
9510 In particular, a relation with a tag will never be considered adjacent
9511 to a relation without a tag.
9513 The function C<isl_schedule_constraints_apply> takes
9514 schedule constraints that are defined on some set of domain elements
9515 and transforms them to schedule constraints on the elements
9516 to which these domain elements are mapped by the given transformation.
9518 An C<isl_schedule_constraints> object can be inspected
9519 using the following functions.
9521 #include <isl/schedule.h>
9522 __isl_give isl_union_set *
9523 isl_schedule_constraints_get_domain(
9524 __isl_keep isl_schedule_constraints *sc);
9525 __isl_give isl_set *isl_schedule_constraints_get_context(
9526 __isl_keep isl_schedule_constraints *sc);
9527 __isl_give isl_union_map *
9528 isl_schedule_constraints_get_validity(
9529 __isl_keep isl_schedule_constraints *sc);
9530 __isl_give isl_union_map *
9531 isl_schedule_constraints_get_coincidence(
9532 __isl_keep isl_schedule_constraints *sc);
9533 __isl_give isl_union_map *
9534 isl_schedule_constraints_get_proximity(
9535 __isl_keep isl_schedule_constraints *sc);
9536 __isl_give isl_union_map *
9537 isl_schedule_constraints_get_conditional_validity(
9538 __isl_keep isl_schedule_constraints *sc);
9539 __isl_give isl_union_map *
9540 isl_schedule_constraints_get_conditional_validity_condition(
9541 __isl_keep isl_schedule_constraints *sc);
9543 An C<isl_schedule_constraints> object can be read from input
9544 using the following functions.
9546 #include <isl/schedule.h>
9547 __isl_give isl_schedule_constraints *
9548 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9550 __isl_give isl_schedule_constraints *
9551 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9554 The contents of an C<isl_schedule_constraints> object can be printed
9555 using the following functions.
9557 #include <isl/schedule.h>
9558 __isl_give isl_printer *
9559 isl_printer_print_schedule_constraints(
9560 __isl_take isl_printer *p,
9561 __isl_keep isl_schedule_constraints *sc);
9562 __isl_give char *isl_schedule_constraints_to_str(
9563 __isl_keep isl_schedule_constraints *sc);
9565 The following function computes a schedule directly from
9566 an iteration domain and validity and proximity dependences
9567 and is implemented in terms of the functions described above.
9568 The use of C<isl_union_set_compute_schedule> is discouraged.
9570 #include <isl/schedule.h>
9571 __isl_give isl_schedule *isl_union_set_compute_schedule(
9572 __isl_take isl_union_set *domain,
9573 __isl_take isl_union_map *validity,
9574 __isl_take isl_union_map *proximity);
9576 The generated schedule represents a schedule tree.
9577 For more information on schedule trees, see
9578 L</"Schedule Trees">.
9582 #include <isl/schedule.h>
9583 isl_stat isl_options_set_schedule_max_coefficient(
9584 isl_ctx *ctx, int val);
9585 int isl_options_get_schedule_max_coefficient(
9587 isl_stat isl_options_set_schedule_max_constant_term(
9588 isl_ctx *ctx, int val);
9589 int isl_options_get_schedule_max_constant_term(
9591 isl_stat isl_options_set_schedule_serialize_sccs(
9592 isl_ctx *ctx, int val);
9593 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9594 isl_stat isl_options_set_schedule_whole_component(
9595 isl_ctx *ctx, int val);
9596 int isl_options_get_schedule_whole_component(
9598 isl_stat isl_options_set_schedule_maximize_band_depth(
9599 isl_ctx *ctx, int val);
9600 int isl_options_get_schedule_maximize_band_depth(
9602 isl_stat isl_options_set_schedule_maximize_coincidence(
9603 isl_ctx *ctx, int val);
9604 int isl_options_get_schedule_maximize_coincidence(
9606 isl_stat isl_options_set_schedule_outer_coincidence(
9607 isl_ctx *ctx, int val);
9608 int isl_options_get_schedule_outer_coincidence(
9610 isl_stat isl_options_set_schedule_split_scaled(
9611 isl_ctx *ctx, int val);
9612 int isl_options_get_schedule_split_scaled(
9614 isl_stat isl_options_set_schedule_treat_coalescing(
9615 isl_ctx *ctx, int val);
9616 int isl_options_get_schedule_treat_coalescing(
9618 isl_stat isl_options_set_schedule_algorithm(
9619 isl_ctx *ctx, int val);
9620 int isl_options_get_schedule_algorithm(
9622 isl_stat isl_options_set_schedule_carry_self_first(
9623 isl_ctx *ctx, int val);
9624 int isl_options_get_schedule_carry_self_first(
9626 isl_stat isl_options_set_schedule_separate_components(
9627 isl_ctx *ctx, int val);
9628 int isl_options_get_schedule_separate_components(
9633 =item * schedule_max_coefficient
9635 This option enforces that the coefficients for variable and parameter
9636 dimensions in the calculated schedule are not larger than the specified value.
9637 This option can significantly increase the speed of the scheduling calculation
9638 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9639 this option does not introduce bounds on the variable or parameter
9642 =item * schedule_max_constant_term
9644 This option enforces that the constant coefficients in the calculated schedule
9645 are not larger than the maximal constant term. This option can significantly
9646 increase the speed of the scheduling calculation and may also prevent fusing of
9647 unrelated dimensions. A value of -1 means that this option does not introduce
9648 bounds on the constant coefficients.
9650 =item * schedule_serialize_sccs
9652 If this option is set, then all strongly connected components
9653 in the dependence graph are serialized as soon as they are detected.
9654 This means in particular that instances of statements will only
9655 appear in the same band node if these statements belong
9656 to the same strongly connected component at the point where
9657 the band node is constructed.
9659 =item * schedule_whole_component
9661 If this option is set, then entire (weakly) connected
9662 components in the dependence graph are scheduled together
9664 Otherwise, each strongly connected component within
9665 such a weakly connected component is first scheduled separately
9666 and then combined with other strongly connected components.
9667 This option has no effect if C<schedule_serialize_sccs> is set.
9669 =item * schedule_maximize_band_depth
9671 If this option is set, then the scheduler tries to maximize
9672 the width of the bands. Wider bands give more possibilities for tiling.
9673 In particular, if the C<schedule_whole_component> option is set,
9674 then bands are split if this might result in wider bands.
9675 Otherwise, the effect of this option is to only allow
9676 strongly connected components to be combined if this does
9677 not reduce the width of the bands.
9678 Note that if the C<schedule_serialize_sccs> options is set, then
9679 the C<schedule_maximize_band_depth> option therefore has no effect.
9681 =item * schedule_maximize_coincidence
9683 This option is only effective if the C<schedule_whole_component>
9684 option is turned off.
9685 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9686 strongly connected components are only combined with each other
9687 if this does not reduce the number of coincident band members.
9689 =item * schedule_outer_coincidence
9691 If this option is set, then we try to construct schedules
9692 where the outermost scheduling dimension in each band
9693 satisfies the coincidence constraints.
9695 =item * schedule_algorithm
9697 Selects the scheduling algorithm to be used.
9698 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9699 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9701 =item * schedule_split_scaled
9703 If this option is set, then we try to construct schedules in which the
9704 constant term is split off from the linear part if the linear parts of
9705 the scheduling rows for all nodes in the graph have a common non-trivial
9707 The constant term is then dropped and the linear
9709 This option is only effective when the Feautrier style scheduler is
9710 being used, either as the main scheduler or as a fallback for the
9711 Pluto-like scheduler.
9713 =item * schedule_treat_coalescing
9715 If this option is set, then the scheduler will try and avoid
9716 producing schedules that perform loop coalescing.
9717 In particular, for the Pluto-like scheduler, this option places
9718 bounds on the schedule coefficients based on the sizes of the instance sets.
9719 For the Feautrier style scheduler, this option detects potentially
9720 coalescing schedules and then tries to adjust the schedule to avoid
9723 =item * schedule_carry_self_first
9725 If this option is set, then the Feautrier style scheduler
9726 (when used as a fallback for the Pluto-like scheduler) will
9727 first try to only carry self-dependences.
9729 =item * schedule_separate_components
9731 If this option is set then the function C<isl_schedule_get_map>
9732 will treat set nodes in the same way as sequence nodes.
9736 =head2 AST Generation
9738 This section describes the C<isl> functionality for generating
9739 ASTs that visit all the elements
9740 in a domain in an order specified by a schedule tree or
9742 In case the schedule given as a C<isl_union_map>, an AST is generated
9743 that visits all the elements in the domain of the C<isl_union_map>
9744 according to the lexicographic order of the corresponding image
9745 element(s). If the range of the C<isl_union_map> consists of
9746 elements in more than one space, then each of these spaces is handled
9747 separately in an arbitrary order.
9748 It should be noted that the schedule tree or the image elements
9749 in a schedule map only specify the I<order>
9750 in which the corresponding domain elements should be visited.
9751 No direct relation between the partial schedule values
9752 or the image elements on the one hand and the loop iterators
9753 in the generated AST on the other hand should be assumed.
9755 Each AST is generated within a build. The initial build
9756 simply specifies the constraints on the parameters (if any)
9757 and can be created, inspected, copied and freed using the following functions.
9759 #include <isl/ast_build.h>
9760 __isl_give isl_ast_build *isl_ast_build_alloc(
9762 __isl_give isl_ast_build *isl_ast_build_from_context(
9763 __isl_take isl_set *set);
9764 __isl_give isl_ast_build *isl_ast_build_copy(
9765 __isl_keep isl_ast_build *build);
9766 __isl_null isl_ast_build *isl_ast_build_free(
9767 __isl_take isl_ast_build *build);
9769 The C<set> argument is usually a parameter set with zero or more parameters.
9770 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9771 this set is required to be a parameter set.
9772 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9773 specify any parameter constraints.
9774 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9775 and L</"Fine-grained Control over AST Generation">.
9776 Finally, the AST itself can be constructed using one of the following
9779 #include <isl/ast_build.h>
9780 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9781 __isl_keep isl_ast_build *build,
9782 __isl_take isl_schedule *schedule);
9783 __isl_give isl_ast_node *
9784 isl_ast_build_node_from_schedule_map(
9785 __isl_keep isl_ast_build *build,
9786 __isl_take isl_union_map *schedule);
9788 =head3 Inspecting the AST
9790 The basic properties of an AST node can be obtained as follows.
9792 #include <isl/ast.h>
9793 enum isl_ast_node_type isl_ast_node_get_type(
9794 __isl_keep isl_ast_node *node);
9796 The type of an AST node is one of
9797 C<isl_ast_node_for>,
9799 C<isl_ast_node_block>,
9800 C<isl_ast_node_mark> or
9801 C<isl_ast_node_user>.
9802 An C<isl_ast_node_for> represents a for node.
9803 An C<isl_ast_node_if> represents an if node.
9804 An C<isl_ast_node_block> represents a compound node.
9805 An C<isl_ast_node_mark> introduces a mark in the AST.
9806 An C<isl_ast_node_user> represents an expression statement.
9807 An expression statement typically corresponds to a domain element, i.e.,
9808 one of the elements that is visited by the AST.
9810 Each type of node has its own additional properties.
9812 #include <isl/ast.h>
9813 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9814 __isl_keep isl_ast_node *node);
9815 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9816 __isl_keep isl_ast_node *node);
9817 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9818 __isl_keep isl_ast_node *node);
9819 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9820 __isl_keep isl_ast_node *node);
9821 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9822 __isl_keep isl_ast_node *node);
9823 isl_bool isl_ast_node_for_is_degenerate(
9824 __isl_keep isl_ast_node *node);
9826 An C<isl_ast_for> is considered degenerate if it is known to execute
9829 #include <isl/ast.h>
9830 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9831 __isl_keep isl_ast_node *node);
9832 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9833 __isl_keep isl_ast_node *node);
9834 isl_bool isl_ast_node_if_has_else(
9835 __isl_keep isl_ast_node *node);
9836 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9837 __isl_keep isl_ast_node *node);
9839 __isl_give isl_ast_node_list *
9840 isl_ast_node_block_get_children(
9841 __isl_keep isl_ast_node *node);
9843 __isl_give isl_id *isl_ast_node_mark_get_id(
9844 __isl_keep isl_ast_node *node);
9845 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9846 __isl_keep isl_ast_node *node);
9848 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9849 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9851 #include <isl/ast.h>
9852 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9853 __isl_keep isl_ast_node *node);
9855 All descendants of a specific node in the AST (including the node itself)
9857 in depth-first pre-order using the following function.
9859 #include <isl/ast.h>
9860 isl_stat isl_ast_node_foreach_descendant_top_down(
9861 __isl_keep isl_ast_node *node,
9862 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9863 void *user), void *user);
9865 The callback function should return C<isl_bool_true> if the children
9866 of the given node should be visited and C<isl_bool_false> if they should not.
9867 It should return C<isl_bool_error> in case of failure, in which case
9868 the entire traversal is aborted.
9870 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9871 the following functions.
9873 #include <isl/ast.h>
9874 enum isl_ast_expr_type isl_ast_expr_get_type(
9875 __isl_keep isl_ast_expr *expr);
9877 The type of an AST expression is one of
9879 C<isl_ast_expr_id> or
9880 C<isl_ast_expr_int>.
9881 An C<isl_ast_expr_op> represents the result of an operation.
9882 An C<isl_ast_expr_id> represents an identifier.
9883 An C<isl_ast_expr_int> represents an integer value.
9885 Each type of expression has its own additional properties.
9887 #include <isl/ast.h>
9888 enum isl_ast_op_type isl_ast_expr_get_op_type(
9889 __isl_keep isl_ast_expr *expr);
9890 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9891 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9892 __isl_keep isl_ast_expr *expr, int pos);
9893 isl_stat isl_ast_expr_foreach_ast_op_type(
9894 __isl_keep isl_ast_expr *expr,
9895 isl_stat (*fn)(enum isl_ast_op_type type,
9896 void *user), void *user);
9897 isl_stat isl_ast_node_foreach_ast_op_type(
9898 __isl_keep isl_ast_node *node,
9899 isl_stat (*fn)(enum isl_ast_op_type type,
9900 void *user), void *user);
9902 C<isl_ast_expr_get_op_type> returns the type of the operation
9903 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9904 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9906 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9907 C<isl_ast_op_type> that appears in C<expr>.
9908 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9909 C<isl_ast_op_type> that appears in C<node>.
9910 The operation type is one of the following.
9914 =item C<isl_ast_op_and>
9916 Logical I<and> of two arguments.
9917 Both arguments can be evaluated.
9919 =item C<isl_ast_op_and_then>
9921 Logical I<and> of two arguments.
9922 The second argument can only be evaluated if the first evaluates to true.
9924 =item C<isl_ast_op_or>
9926 Logical I<or> of two arguments.
9927 Both arguments can be evaluated.
9929 =item C<isl_ast_op_or_else>
9931 Logical I<or> of two arguments.
9932 The second argument can only be evaluated if the first evaluates to false.
9934 =item C<isl_ast_op_max>
9936 Maximum of two or more arguments.
9938 =item C<isl_ast_op_min>
9940 Minimum of two or more arguments.
9942 =item C<isl_ast_op_minus>
9946 =item C<isl_ast_op_add>
9948 Sum of two arguments.
9950 =item C<isl_ast_op_sub>
9952 Difference of two arguments.
9954 =item C<isl_ast_op_mul>
9956 Product of two arguments.
9958 =item C<isl_ast_op_div>
9960 Exact division. That is, the result is known to be an integer.
9962 =item C<isl_ast_op_fdiv_q>
9964 Result of integer division, rounded towards negative
9966 The divisor is known to be positive.
9968 =item C<isl_ast_op_pdiv_q>
9970 Result of integer division, where dividend is known to be non-negative.
9971 The divisor is known to be positive.
9973 =item C<isl_ast_op_pdiv_r>
9975 Remainder of integer division, where dividend is known to be non-negative.
9976 The divisor is known to be positive.
9978 =item C<isl_ast_op_zdiv_r>
9980 Equal to zero iff the remainder on integer division is zero.
9981 The divisor is known to be positive.
9983 =item C<isl_ast_op_cond>
9985 Conditional operator defined on three arguments.
9986 If the first argument evaluates to true, then the result
9987 is equal to the second argument. Otherwise, the result
9988 is equal to the third argument.
9989 The second and third argument may only be evaluated if
9990 the first argument evaluates to true and false, respectively.
9991 Corresponds to C<a ? b : c> in C.
9993 =item C<isl_ast_op_select>
9995 Conditional operator defined on three arguments.
9996 If the first argument evaluates to true, then the result
9997 is equal to the second argument. Otherwise, the result
9998 is equal to the third argument.
9999 The second and third argument may be evaluated independently
10000 of the value of the first argument.
10001 Corresponds to C<a * b + (1 - a) * c> in C.
10003 =item C<isl_ast_op_eq>
10007 =item C<isl_ast_op_le>
10009 Less than or equal relation.
10011 =item C<isl_ast_op_lt>
10013 Less than relation.
10015 =item C<isl_ast_op_ge>
10017 Greater than or equal relation.
10019 =item C<isl_ast_op_gt>
10021 Greater than relation.
10023 =item C<isl_ast_op_call>
10026 The number of arguments of the C<isl_ast_expr> is one more than
10027 the number of arguments in the function call, the first argument
10028 representing the function being called.
10030 =item C<isl_ast_op_access>
10033 The number of arguments of the C<isl_ast_expr> is one more than
10034 the number of index expressions in the array access, the first argument
10035 representing the array being accessed.
10037 =item C<isl_ast_op_member>
10040 This operation has two arguments, a structure and the name of
10041 the member of the structure being accessed.
10045 #include <isl/ast.h>
10046 __isl_give isl_id *isl_ast_expr_get_id(
10047 __isl_keep isl_ast_expr *expr);
10049 Return the identifier represented by the AST expression.
10051 #include <isl/ast.h>
10052 __isl_give isl_val *isl_ast_expr_get_val(
10053 __isl_keep isl_ast_expr *expr);
10055 Return the integer represented by the AST expression.
10057 =head3 Properties of ASTs
10059 #include <isl/ast.h>
10060 isl_bool isl_ast_expr_is_equal(
10061 __isl_keep isl_ast_expr *expr1,
10062 __isl_keep isl_ast_expr *expr2);
10064 Check if two C<isl_ast_expr>s are equal to each other.
10066 =head3 Manipulating and printing the AST
10068 AST nodes can be copied and freed using the following functions.
10070 #include <isl/ast.h>
10071 __isl_give isl_ast_node *isl_ast_node_copy(
10072 __isl_keep isl_ast_node *node);
10073 __isl_null isl_ast_node *isl_ast_node_free(
10074 __isl_take isl_ast_node *node);
10076 AST expressions can be copied and freed using the following functions.
10078 #include <isl/ast.h>
10079 __isl_give isl_ast_expr *isl_ast_expr_copy(
10080 __isl_keep isl_ast_expr *expr);
10081 __isl_null isl_ast_expr *isl_ast_expr_free(
10082 __isl_take isl_ast_expr *expr);
10084 New AST expressions can be created either directly or within
10085 the context of an C<isl_ast_build>.
10087 #include <isl/ast.h>
10088 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10089 __isl_take isl_val *v);
10090 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10091 __isl_take isl_id *id);
10092 __isl_give isl_ast_expr *isl_ast_expr_neg(
10093 __isl_take isl_ast_expr *expr);
10094 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10095 __isl_take isl_ast_expr *expr);
10096 __isl_give isl_ast_expr *isl_ast_expr_add(
10097 __isl_take isl_ast_expr *expr1,
10098 __isl_take isl_ast_expr *expr2);
10099 __isl_give isl_ast_expr *isl_ast_expr_sub(
10100 __isl_take isl_ast_expr *expr1,
10101 __isl_take isl_ast_expr *expr2);
10102 __isl_give isl_ast_expr *isl_ast_expr_mul(
10103 __isl_take isl_ast_expr *expr1,
10104 __isl_take isl_ast_expr *expr2);
10105 __isl_give isl_ast_expr *isl_ast_expr_div(
10106 __isl_take isl_ast_expr *expr1,
10107 __isl_take isl_ast_expr *expr2);
10108 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10109 __isl_take isl_ast_expr *expr1,
10110 __isl_take isl_ast_expr *expr2);
10111 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10112 __isl_take isl_ast_expr *expr1,
10113 __isl_take isl_ast_expr *expr2);
10114 __isl_give isl_ast_expr *isl_ast_expr_and(
10115 __isl_take isl_ast_expr *expr1,
10116 __isl_take isl_ast_expr *expr2)
10117 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10118 __isl_take isl_ast_expr *expr1,
10119 __isl_take isl_ast_expr *expr2)
10120 __isl_give isl_ast_expr *isl_ast_expr_or(
10121 __isl_take isl_ast_expr *expr1,
10122 __isl_take isl_ast_expr *expr2)
10123 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10124 __isl_take isl_ast_expr *expr1,
10125 __isl_take isl_ast_expr *expr2)
10126 __isl_give isl_ast_expr *isl_ast_expr_eq(
10127 __isl_take isl_ast_expr *expr1,
10128 __isl_take isl_ast_expr *expr2);
10129 __isl_give isl_ast_expr *isl_ast_expr_le(
10130 __isl_take isl_ast_expr *expr1,
10131 __isl_take isl_ast_expr *expr2);
10132 __isl_give isl_ast_expr *isl_ast_expr_lt(
10133 __isl_take isl_ast_expr *expr1,
10134 __isl_take isl_ast_expr *expr2);
10135 __isl_give isl_ast_expr *isl_ast_expr_ge(
10136 __isl_take isl_ast_expr *expr1,
10137 __isl_take isl_ast_expr *expr2);
10138 __isl_give isl_ast_expr *isl_ast_expr_gt(
10139 __isl_take isl_ast_expr *expr1,
10140 __isl_take isl_ast_expr *expr2);
10141 __isl_give isl_ast_expr *isl_ast_expr_access(
10142 __isl_take isl_ast_expr *array,
10143 __isl_take isl_ast_expr_list *indices);
10144 __isl_give isl_ast_expr *isl_ast_expr_call(
10145 __isl_take isl_ast_expr *function,
10146 __isl_take isl_ast_expr_list *arguments);
10148 The function C<isl_ast_expr_address_of> can be applied to an
10149 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10150 to represent the address of the C<isl_ast_expr_access>.
10151 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10152 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10154 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10155 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10157 #include <isl/ast_build.h>
10158 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10159 __isl_keep isl_ast_build *build,
10160 __isl_take isl_set *set);
10161 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10162 __isl_keep isl_ast_build *build,
10163 __isl_take isl_pw_aff *pa);
10164 __isl_give isl_ast_expr *
10165 isl_ast_build_access_from_pw_multi_aff(
10166 __isl_keep isl_ast_build *build,
10167 __isl_take isl_pw_multi_aff *pma);
10168 __isl_give isl_ast_expr *
10169 isl_ast_build_access_from_multi_pw_aff(
10170 __isl_keep isl_ast_build *build,
10171 __isl_take isl_multi_pw_aff *mpa);
10172 __isl_give isl_ast_expr *
10173 isl_ast_build_call_from_pw_multi_aff(
10174 __isl_keep isl_ast_build *build,
10175 __isl_take isl_pw_multi_aff *pma);
10176 __isl_give isl_ast_expr *
10177 isl_ast_build_call_from_multi_pw_aff(
10178 __isl_keep isl_ast_build *build,
10179 __isl_take isl_multi_pw_aff *mpa);
10182 the domains of C<pa>, C<mpa> and C<pma> should correspond
10183 to the schedule space of C<build>.
10184 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10185 the function being called.
10186 If the accessed space is a nested relation, then it is taken
10187 to represent an access of the member specified by the range
10188 of this nested relation of the structure specified by the domain
10189 of the nested relation.
10191 The following functions can be used to modify an C<isl_ast_expr>.
10193 #include <isl/ast.h>
10194 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10195 __isl_take isl_ast_expr *expr, int pos,
10196 __isl_take isl_ast_expr *arg);
10198 Replace the argument of C<expr> at position C<pos> by C<arg>.
10200 #include <isl/ast.h>
10201 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10202 __isl_take isl_ast_expr *expr,
10203 __isl_take isl_id_to_ast_expr *id2expr);
10205 The function C<isl_ast_expr_substitute_ids> replaces the
10206 subexpressions of C<expr> of type C<isl_ast_expr_id>
10207 by the corresponding expression in C<id2expr>, if there is any.
10210 User specified data can be attached to an C<isl_ast_node> and obtained
10211 from the same C<isl_ast_node> using the following functions.
10213 #include <isl/ast.h>
10214 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10215 __isl_take isl_ast_node *node,
10216 __isl_take isl_id *annotation);
10217 __isl_give isl_id *isl_ast_node_get_annotation(
10218 __isl_keep isl_ast_node *node);
10220 Basic printing can be performed using the following functions.
10222 #include <isl/ast.h>
10223 __isl_give isl_printer *isl_printer_print_ast_expr(
10224 __isl_take isl_printer *p,
10225 __isl_keep isl_ast_expr *expr);
10226 __isl_give isl_printer *isl_printer_print_ast_node(
10227 __isl_take isl_printer *p,
10228 __isl_keep isl_ast_node *node);
10229 __isl_give char *isl_ast_expr_to_str(
10230 __isl_keep isl_ast_expr *expr);
10231 __isl_give char *isl_ast_node_to_str(
10232 __isl_keep isl_ast_node *node);
10233 __isl_give char *isl_ast_expr_to_C_str(
10234 __isl_keep isl_ast_expr *expr);
10235 __isl_give char *isl_ast_node_to_C_str(
10236 __isl_keep isl_ast_node *node);
10238 The functions C<isl_ast_expr_to_C_str> and
10239 C<isl_ast_node_to_C_str> are convenience functions
10240 that return a string representation of the input in C format.
10242 More advanced printing can be performed using the following functions.
10244 #include <isl/ast.h>
10245 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10246 __isl_take isl_printer *p,
10247 enum isl_ast_op_type type,
10248 __isl_keep const char *name);
10249 isl_stat isl_options_set_ast_print_macro_once(
10250 isl_ctx *ctx, int val);
10251 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10252 __isl_give isl_printer *isl_ast_op_type_print_macro(
10253 enum isl_ast_op_type type,
10254 __isl_take isl_printer *p);
10255 __isl_give isl_printer *isl_ast_expr_print_macros(
10256 __isl_keep isl_ast_expr *expr,
10257 __isl_take isl_printer *p);
10258 __isl_give isl_printer *isl_ast_node_print_macros(
10259 __isl_keep isl_ast_node *node,
10260 __isl_take isl_printer *p);
10261 __isl_give isl_printer *isl_ast_node_print(
10262 __isl_keep isl_ast_node *node,
10263 __isl_take isl_printer *p,
10264 __isl_take isl_ast_print_options *options);
10265 __isl_give isl_printer *isl_ast_node_for_print(
10266 __isl_keep isl_ast_node *node,
10267 __isl_take isl_printer *p,
10268 __isl_take isl_ast_print_options *options);
10269 __isl_give isl_printer *isl_ast_node_if_print(
10270 __isl_keep isl_ast_node *node,
10271 __isl_take isl_printer *p,
10272 __isl_take isl_ast_print_options *options);
10274 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10275 C<isl> may print out an AST that makes use of macros such
10276 as C<floord>, C<min> and C<max>.
10277 The names of these macros may be modified by a call
10278 to C<isl_ast_op_type_set_print_name>. The user-specified
10279 names are associated to the printer object.
10280 C<isl_ast_op_type_print_macro> prints out the macro
10281 corresponding to a specific C<isl_ast_op_type>.
10282 If the print-macro-once option is set, then a given macro definition
10283 is only printed once to any given printer object.
10284 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10285 for subexpressions where these macros would be used and prints
10286 out the required macro definitions.
10287 Essentially, C<isl_ast_expr_print_macros> calls
10288 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10289 as function argument.
10290 C<isl_ast_node_print_macros> does the same
10291 for expressions in its C<isl_ast_node> argument.
10292 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10293 C<isl_ast_node_if_print> print an C<isl_ast_node>
10294 in C<ISL_FORMAT_C>, but allow for some extra control
10295 through an C<isl_ast_print_options> object.
10296 This object can be created using the following functions.
10298 #include <isl/ast.h>
10299 __isl_give isl_ast_print_options *
10300 isl_ast_print_options_alloc(isl_ctx *ctx);
10301 __isl_give isl_ast_print_options *
10302 isl_ast_print_options_copy(
10303 __isl_keep isl_ast_print_options *options);
10304 __isl_null isl_ast_print_options *
10305 isl_ast_print_options_free(
10306 __isl_take isl_ast_print_options *options);
10308 __isl_give isl_ast_print_options *
10309 isl_ast_print_options_set_print_user(
10310 __isl_take isl_ast_print_options *options,
10311 __isl_give isl_printer *(*print_user)(
10312 __isl_take isl_printer *p,
10313 __isl_take isl_ast_print_options *options,
10314 __isl_keep isl_ast_node *node, void *user),
10316 __isl_give isl_ast_print_options *
10317 isl_ast_print_options_set_print_for(
10318 __isl_take isl_ast_print_options *options,
10319 __isl_give isl_printer *(*print_for)(
10320 __isl_take isl_printer *p,
10321 __isl_take isl_ast_print_options *options,
10322 __isl_keep isl_ast_node *node, void *user),
10325 The callback set by C<isl_ast_print_options_set_print_user>
10326 is called whenever a node of type C<isl_ast_node_user> needs to
10328 The callback set by C<isl_ast_print_options_set_print_for>
10329 is called whenever a node of type C<isl_ast_node_for> needs to
10331 Note that C<isl_ast_node_for_print> will I<not> call the
10332 callback set by C<isl_ast_print_options_set_print_for> on the node
10333 on which C<isl_ast_node_for_print> is called, but only on nested
10334 nodes of type C<isl_ast_node_for>. It is therefore safe to
10335 call C<isl_ast_node_for_print> from within the callback set by
10336 C<isl_ast_print_options_set_print_for>.
10338 The following option determines the type to be used for iterators
10339 while printing the AST.
10341 isl_stat isl_options_set_ast_iterator_type(
10342 isl_ctx *ctx, const char *val);
10343 const char *isl_options_get_ast_iterator_type(
10346 The AST printer only prints body nodes as blocks if these
10347 blocks cannot be safely omitted.
10348 For example, a C<for> node with one body node will not be
10349 surrounded with braces in C<ISL_FORMAT_C>.
10350 A block will always be printed by setting the following option.
10352 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10354 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10358 #include <isl/ast_build.h>
10359 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10360 isl_ctx *ctx, int val);
10361 int isl_options_get_ast_build_atomic_upper_bound(
10363 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10365 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10366 isl_stat isl_options_set_ast_build_detect_min_max(
10367 isl_ctx *ctx, int val);
10368 int isl_options_get_ast_build_detect_min_max(
10370 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10371 isl_ctx *ctx, int val);
10372 int isl_options_get_ast_build_exploit_nested_bounds(
10374 isl_stat isl_options_set_ast_build_group_coscheduled(
10375 isl_ctx *ctx, int val);
10376 int isl_options_get_ast_build_group_coscheduled(
10378 isl_stat isl_options_set_ast_build_separation_bounds(
10379 isl_ctx *ctx, int val);
10380 int isl_options_get_ast_build_separation_bounds(
10382 isl_stat isl_options_set_ast_build_scale_strides(
10383 isl_ctx *ctx, int val);
10384 int isl_options_get_ast_build_scale_strides(
10386 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10388 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10389 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10391 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10395 =item * ast_build_atomic_upper_bound
10397 Generate loop upper bounds that consist of the current loop iterator,
10398 an operator and an expression not involving the iterator.
10399 If this option is not set, then the current loop iterator may appear
10400 several times in the upper bound.
10401 For example, when this option is turned off, AST generation
10404 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10408 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10411 When the option is turned on, the following AST is generated
10413 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10416 =item * ast_build_prefer_pdiv
10418 If this option is turned off, then the AST generation will
10419 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10420 operators, but no C<isl_ast_op_pdiv_q> or
10421 C<isl_ast_op_pdiv_r> operators.
10422 If this option is turned on, then C<isl> will try to convert
10423 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10424 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10426 =item * ast_build_detect_min_max
10428 If this option is turned on, then C<isl> will try and detect
10429 min or max-expressions when building AST expressions from
10430 piecewise affine expressions.
10432 =item * ast_build_exploit_nested_bounds
10434 Simplify conditions based on bounds of nested for loops.
10435 In particular, remove conditions that are implied by the fact
10436 that one or more nested loops have at least one iteration,
10437 meaning that the upper bound is at least as large as the lower bound.
10438 For example, when this option is turned off, AST generation
10441 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10447 for (int c0 = 0; c0 <= N; c0 += 1)
10448 for (int c1 = 0; c1 <= M; c1 += 1)
10451 When the option is turned on, the following AST is generated
10453 for (int c0 = 0; c0 <= N; c0 += 1)
10454 for (int c1 = 0; c1 <= M; c1 += 1)
10457 =item * ast_build_group_coscheduled
10459 If two domain elements are assigned the same schedule point, then
10460 they may be executed in any order and they may even appear in different
10461 loops. If this options is set, then the AST generator will make
10462 sure that coscheduled domain elements do not appear in separate parts
10463 of the AST. This is useful in case of nested AST generation
10464 if the outer AST generation is given only part of a schedule
10465 and the inner AST generation should handle the domains that are
10466 coscheduled by this initial part of the schedule together.
10467 For example if an AST is generated for a schedule
10469 { A[i] -> [0]; B[i] -> [0] }
10471 then the C<isl_ast_build_set_create_leaf> callback described
10472 below may get called twice, once for each domain.
10473 Setting this option ensures that the callback is only called once
10474 on both domains together.
10476 =item * ast_build_separation_bounds
10478 This option specifies which bounds to use during separation.
10479 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10480 then all (possibly implicit) bounds on the current dimension will
10481 be used during separation.
10482 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10483 then only those bounds that are explicitly available will
10484 be used during separation.
10486 =item * ast_build_scale_strides
10488 This option specifies whether the AST generator is allowed
10489 to scale down iterators of strided loops.
10491 =item * ast_build_allow_else
10493 This option specifies whether the AST generator is allowed
10494 to construct if statements with else branches.
10496 =item * ast_build_allow_or
10498 This option specifies whether the AST generator is allowed
10499 to construct if conditions with disjunctions.
10503 =head3 AST Generation Options (Schedule Tree)
10505 In case of AST construction from a schedule tree, the options
10506 that control how an AST is created from the individual schedule
10507 dimensions are stored in the band nodes of the tree
10508 (see L</"Schedule Trees">).
10510 In particular, a schedule dimension can be handled in four
10511 different ways, atomic, separate, unroll or the default.
10512 This loop AST generation type can be set using
10513 C<isl_schedule_node_band_member_set_ast_loop_type>.
10515 the first three can be selected by including a one-dimensional
10516 element with as value the position of the schedule dimension
10517 within the band and as name one of C<atomic>, C<separate>
10518 or C<unroll> in the options
10519 set by C<isl_schedule_node_band_set_ast_build_options>.
10520 Only one of these three may be specified for
10521 any given schedule dimension within a band node.
10522 If none of these is specified, then the default
10523 is used. The meaning of the options is as follows.
10529 When this option is specified, the AST generator will make
10530 sure that a given domains space only appears in a single
10531 loop at the specified level.
10533 For example, for the schedule tree
10535 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10537 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10538 options: "{ atomic[x] }"
10540 the following AST will be generated
10542 for (int c0 = 0; c0 <= 10; c0 += 1) {
10549 On the other hand, for the schedule tree
10551 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10553 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10554 options: "{ separate[x] }"
10556 the following AST will be generated
10560 for (int c0 = 1; c0 <= 9; c0 += 1) {
10567 If neither C<atomic> nor C<separate> is specified, then the AST generator
10568 may produce either of these two results or some intermediate form.
10572 When this option is specified, the AST generator will
10573 split the domain of the specified schedule dimension
10574 into pieces with a fixed set of statements for which
10575 instances need to be executed by the iterations in
10576 the schedule domain part. This option tends to avoid
10577 the generation of guards inside the corresponding loops.
10578 See also the C<atomic> option.
10582 When this option is specified, the AST generator will
10583 I<completely> unroll the corresponding schedule dimension.
10584 It is the responsibility of the user to ensure that such
10585 unrolling is possible.
10586 To obtain a partial unrolling, the user should apply an additional
10587 strip-mining to the schedule and fully unroll the inner schedule
10592 The C<isolate> option is a bit more involved. It allows the user
10593 to isolate a range of schedule dimension values from smaller and
10594 greater values. Additionally, the user may specify a different
10595 atomic/separate/unroll choice for the isolated part and the remaining
10596 parts. The typical use case of the C<isolate> option is to isolate
10597 full tiles from partial tiles.
10598 The part that needs to be isolated may depend on outer schedule dimensions.
10599 The option therefore needs to be able to reference those outer schedule
10600 dimensions. In particular, the space of the C<isolate> option is that
10601 of a wrapped map with as domain the flat product of all outer band nodes
10602 and as range the space of the current band node.
10603 The atomic/separate/unroll choice for the isolated part is determined
10604 by an option that lives in an unnamed wrapped space with as domain
10605 a zero-dimensional C<isolate> space and as range the regular
10606 C<atomic>, C<separate> or C<unroll> space.
10607 This option may also be set directly using
10608 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10609 The atomic/separate/unroll choice for the remaining part is determined
10610 by the regular C<atomic>, C<separate> or C<unroll> option.
10611 Since the C<isolate> option references outer schedule dimensions,
10612 its use in a band node causes any tree containing the node
10613 to be considered anchored.
10615 As an example, consider the isolation of full tiles from partial tiles
10616 in a tiling of a triangular domain. The original schedule is as follows.
10618 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10620 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10621 { A[i,j] -> [floor(j/10)] }, \
10622 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10626 for (int c0 = 0; c0 <= 10; c0 += 1)
10627 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10628 for (int c2 = 10 * c0;
10629 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10630 for (int c3 = 10 * c1;
10631 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10634 Isolating the full tiles, we have the following input
10636 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10638 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10639 { A[i,j] -> [floor(j/10)] }, \
10640 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10641 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10642 10a+9+10b+9 <= 100 }"
10647 for (int c0 = 0; c0 <= 8; c0 += 1) {
10648 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10649 for (int c2 = 10 * c0;
10650 c2 <= 10 * c0 + 9; c2 += 1)
10651 for (int c3 = 10 * c1;
10652 c3 <= 10 * c1 + 9; c3 += 1)
10654 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10655 for (int c2 = 10 * c0;
10656 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10657 for (int c3 = 10 * c1;
10658 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10661 for (int c0 = 9; c0 <= 10; c0 += 1)
10662 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10663 for (int c2 = 10 * c0;
10664 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10665 for (int c3 = 10 * c1;
10666 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10670 We may then additionally unroll the innermost loop of the isolated part
10672 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10674 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10675 { A[i,j] -> [floor(j/10)] }, \
10676 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10677 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10678 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10683 for (int c0 = 0; c0 <= 8; c0 += 1) {
10684 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10685 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10687 A(c2, 10 * c1 + 1);
10688 A(c2, 10 * c1 + 2);
10689 A(c2, 10 * c1 + 3);
10690 A(c2, 10 * c1 + 4);
10691 A(c2, 10 * c1 + 5);
10692 A(c2, 10 * c1 + 6);
10693 A(c2, 10 * c1 + 7);
10694 A(c2, 10 * c1 + 8);
10695 A(c2, 10 * c1 + 9);
10697 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10698 for (int c2 = 10 * c0;
10699 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10700 for (int c3 = 10 * c1;
10701 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10704 for (int c0 = 9; c0 <= 10; c0 += 1)
10705 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10706 for (int c2 = 10 * c0;
10707 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10708 for (int c3 = 10 * c1;
10709 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10714 =head3 AST Generation Options (Schedule Map)
10716 In case of AST construction using
10717 C<isl_ast_build_node_from_schedule_map>, the options
10718 that control how an AST is created from the individual schedule
10719 dimensions are stored in the C<isl_ast_build>.
10720 They can be set using the following function.
10722 #include <isl/ast_build.h>
10723 __isl_give isl_ast_build *
10724 isl_ast_build_set_options(
10725 __isl_take isl_ast_build *build,
10726 __isl_take isl_union_map *options);
10728 The options are encoded in an C<isl_union_map>.
10729 The domain of this union relation refers to the schedule domain,
10730 i.e., the range of the schedule passed
10731 to C<isl_ast_build_node_from_schedule_map>.
10732 In the case of nested AST generation (see L</"Nested AST Generation">),
10733 the domain of C<options> should refer to the extra piece of the schedule.
10734 That is, it should be equal to the range of the wrapped relation in the
10735 range of the schedule.
10736 The range of the options can consist of elements in one or more spaces,
10737 the names of which determine the effect of the option.
10738 The values of the range typically also refer to the schedule dimension
10739 to which the option applies, with value C<0> representing
10740 the outermost schedule dimension. In case of nested AST generation
10741 (see L</"Nested AST Generation">), these values refer to the position
10742 of the schedule dimension within the innermost AST generation.
10743 The constraints on the domain elements of
10744 the option should only refer to this dimension and earlier dimensions.
10745 We consider the following spaces.
10749 =item C<separation_class>
10751 B<This option has been deprecated. Use the isolate option on
10752 schedule trees instead.>
10754 This space is a wrapped relation between two one dimensional spaces.
10755 The input space represents the schedule dimension to which the option
10756 applies and the output space represents the separation class.
10757 While constructing a loop corresponding to the specified schedule
10758 dimension(s), the AST generator will try to generate separate loops
10759 for domain elements that are assigned different classes.
10760 If only some of the elements are assigned a class, then those elements
10761 that are not assigned any class will be treated as belonging to a class
10762 that is separate from the explicitly assigned classes.
10763 The typical use case for this option is to separate full tiles from
10765 The other options, described below, are applied after the separation
10768 As an example, consider the separation into full and partial tiles
10769 of a tiling of a triangular domain.
10770 Take, for example, the domain
10772 { A[i,j] : 0 <= i,j and i + j <= 100 }
10774 and a tiling into tiles of 10 by 10. The input to the AST generator
10775 is then the schedule
10777 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10780 Without any options, the following AST is generated
10782 for (int c0 = 0; c0 <= 10; c0 += 1)
10783 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10784 for (int c2 = 10 * c0;
10785 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10787 for (int c3 = 10 * c1;
10788 c3 <= min(10 * c1 + 9, -c2 + 100);
10792 Separation into full and partial tiles can be obtained by assigning
10793 a class, say C<0>, to the full tiles. The full tiles are represented by those
10794 values of the first and second schedule dimensions for which there are
10795 values of the third and fourth dimensions to cover an entire tile.
10796 That is, we need to specify the following option
10798 { [a,b,c,d] -> separation_class[[0]->[0]] :
10799 exists b': 0 <= 10a,10b' and
10800 10a+9+10b'+9 <= 100;
10801 [a,b,c,d] -> separation_class[[1]->[0]] :
10802 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10804 which simplifies to
10806 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10807 a >= 0 and b >= 0 and b <= 8 - a;
10808 [a, b, c, d] -> separation_class[[0] -> [0]] :
10809 a >= 0 and a <= 8 }
10811 With this option, the generated AST is as follows
10814 for (int c0 = 0; c0 <= 8; c0 += 1) {
10815 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10816 for (int c2 = 10 * c0;
10817 c2 <= 10 * c0 + 9; c2 += 1)
10818 for (int c3 = 10 * c1;
10819 c3 <= 10 * c1 + 9; c3 += 1)
10821 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10822 for (int c2 = 10 * c0;
10823 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10825 for (int c3 = 10 * c1;
10826 c3 <= min(-c2 + 100, 10 * c1 + 9);
10830 for (int c0 = 9; c0 <= 10; c0 += 1)
10831 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10832 for (int c2 = 10 * c0;
10833 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10835 for (int c3 = 10 * c1;
10836 c3 <= min(10 * c1 + 9, -c2 + 100);
10843 This is a single-dimensional space representing the schedule dimension(s)
10844 to which ``separation'' should be applied. Separation tries to split
10845 a loop into several pieces if this can avoid the generation of guards
10847 See also the C<atomic> option.
10851 This is a single-dimensional space representing the schedule dimension(s)
10852 for which the domains should be considered ``atomic''. That is, the
10853 AST generator will make sure that any given domain space will only appear
10854 in a single loop at the specified level.
10856 Consider the following schedule
10858 { a[i] -> [i] : 0 <= i < 10;
10859 b[i] -> [i+1] : 0 <= i < 10 }
10861 If the following option is specified
10863 { [i] -> separate[x] }
10865 then the following AST will be generated
10869 for (int c0 = 1; c0 <= 9; c0 += 1) {
10876 If, on the other hand, the following option is specified
10878 { [i] -> atomic[x] }
10880 then the following AST will be generated
10882 for (int c0 = 0; c0 <= 10; c0 += 1) {
10889 If neither C<atomic> nor C<separate> is specified, then the AST generator
10890 may produce either of these two results or some intermediate form.
10894 This is a single-dimensional space representing the schedule dimension(s)
10895 that should be I<completely> unrolled.
10896 To obtain a partial unrolling, the user should apply an additional
10897 strip-mining to the schedule and fully unroll the inner loop.
10901 =head3 Fine-grained Control over AST Generation
10903 Besides specifying the constraints on the parameters,
10904 an C<isl_ast_build> object can be used to control
10905 various aspects of the AST generation process.
10906 In case of AST construction using
10907 C<isl_ast_build_node_from_schedule_map>,
10908 the most prominent way of control is through ``options'',
10909 as explained above.
10911 Additional control is available through the following functions.
10913 #include <isl/ast_build.h>
10914 __isl_give isl_ast_build *
10915 isl_ast_build_set_iterators(
10916 __isl_take isl_ast_build *build,
10917 __isl_take isl_id_list *iterators);
10919 The function C<isl_ast_build_set_iterators> allows the user to
10920 specify a list of iterator C<isl_id>s to be used as iterators.
10921 If the input schedule is injective, then
10922 the number of elements in this list should be as large as the dimension
10923 of the schedule space, but no direct correspondence should be assumed
10924 between dimensions and elements.
10925 If the input schedule is not injective, then an additional number
10926 of C<isl_id>s equal to the largest dimension of the input domains
10928 If the number of provided C<isl_id>s is insufficient, then additional
10929 names are automatically generated.
10931 #include <isl/ast_build.h>
10932 __isl_give isl_ast_build *
10933 isl_ast_build_set_create_leaf(
10934 __isl_take isl_ast_build *build,
10935 __isl_give isl_ast_node *(*fn)(
10936 __isl_take isl_ast_build *build,
10937 void *user), void *user);
10940 C<isl_ast_build_set_create_leaf> function allows for the
10941 specification of a callback that should be called whenever the AST
10942 generator arrives at an element of the schedule domain.
10943 The callback should return an AST node that should be inserted
10944 at the corresponding position of the AST. The default action (when
10945 the callback is not set) is to continue generating parts of the AST to scan
10946 all the domain elements associated to the schedule domain element
10947 and to insert user nodes, ``calling'' the domain element, for each of them.
10948 The C<build> argument contains the current state of the C<isl_ast_build>.
10949 To ease nested AST generation (see L</"Nested AST Generation">),
10950 all control information that is
10951 specific to the current AST generation such as the options and
10952 the callbacks has been removed from this C<isl_ast_build>.
10953 The callback would typically return the result of a nested
10954 AST generation or a
10955 user defined node created using the following function.
10957 #include <isl/ast.h>
10958 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10959 __isl_take isl_ast_expr *expr);
10961 #include <isl/ast_build.h>
10962 __isl_give isl_ast_build *
10963 isl_ast_build_set_at_each_domain(
10964 __isl_take isl_ast_build *build,
10965 __isl_give isl_ast_node *(*fn)(
10966 __isl_take isl_ast_node *node,
10967 __isl_keep isl_ast_build *build,
10968 void *user), void *user);
10969 __isl_give isl_ast_build *
10970 isl_ast_build_set_before_each_for(
10971 __isl_take isl_ast_build *build,
10972 __isl_give isl_id *(*fn)(
10973 __isl_keep isl_ast_build *build,
10974 void *user), void *user);
10975 __isl_give isl_ast_build *
10976 isl_ast_build_set_after_each_for(
10977 __isl_take isl_ast_build *build,
10978 __isl_give isl_ast_node *(*fn)(
10979 __isl_take isl_ast_node *node,
10980 __isl_keep isl_ast_build *build,
10981 void *user), void *user);
10982 __isl_give isl_ast_build *
10983 isl_ast_build_set_before_each_mark(
10984 __isl_take isl_ast_build *build,
10985 isl_stat (*fn)(__isl_keep isl_id *mark,
10986 __isl_keep isl_ast_build *build,
10987 void *user), void *user);
10988 __isl_give isl_ast_build *
10989 isl_ast_build_set_after_each_mark(
10990 __isl_take isl_ast_build *build,
10991 __isl_give isl_ast_node *(*fn)(
10992 __isl_take isl_ast_node *node,
10993 __isl_keep isl_ast_build *build,
10994 void *user), void *user);
10996 The callback set by C<isl_ast_build_set_at_each_domain> will
10997 be called for each domain AST node.
10998 The callbacks set by C<isl_ast_build_set_before_each_for>
10999 and C<isl_ast_build_set_after_each_for> will be called
11000 for each for AST node. The first will be called in depth-first
11001 pre-order, while the second will be called in depth-first post-order.
11002 Since C<isl_ast_build_set_before_each_for> is called before the for
11003 node is actually constructed, it is only passed an C<isl_ast_build>.
11004 The returned C<isl_id> will be added as an annotation (using
11005 C<isl_ast_node_set_annotation>) to the constructed for node.
11006 In particular, if the user has also specified an C<after_each_for>
11007 callback, then the annotation can be retrieved from the node passed to
11008 that callback using C<isl_ast_node_get_annotation>.
11009 The callbacks set by C<isl_ast_build_set_before_each_mark>
11010 and C<isl_ast_build_set_after_each_mark> will be called for each
11011 mark AST node that is created, i.e., for each mark schedule node
11012 in the input schedule tree. The first will be called in depth-first
11013 pre-order, while the second will be called in depth-first post-order.
11014 Since the callback set by C<isl_ast_build_set_before_each_mark>
11015 is called before the mark AST node is actually constructed, it is passed
11016 the identifier of the mark node.
11017 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11018 The given C<isl_ast_build> can be used to create new
11019 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11020 or C<isl_ast_build_call_from_pw_multi_aff>.
11022 =head3 Nested AST Generation
11024 C<isl> allows the user to create an AST within the context
11025 of another AST. These nested ASTs are created using the
11026 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11027 the outer AST. The C<build> argument should be an C<isl_ast_build>
11028 passed to a callback set by
11029 C<isl_ast_build_set_create_leaf>.
11030 The space of the range of the C<schedule> argument should refer
11031 to this build. In particular, the space should be a wrapped
11032 relation and the domain of this wrapped relation should be the
11033 same as that of the range of the schedule returned by
11034 C<isl_ast_build_get_schedule> below.
11035 In practice, the new schedule is typically
11036 created by calling C<isl_union_map_range_product> on the old schedule
11037 and some extra piece of the schedule.
11038 The space of the schedule domain is also available from
11039 the C<isl_ast_build>.
11041 #include <isl/ast_build.h>
11042 __isl_give isl_union_map *isl_ast_build_get_schedule(
11043 __isl_keep isl_ast_build *build);
11044 __isl_give isl_space *isl_ast_build_get_schedule_space(
11045 __isl_keep isl_ast_build *build);
11046 __isl_give isl_ast_build *isl_ast_build_restrict(
11047 __isl_take isl_ast_build *build,
11048 __isl_take isl_set *set);
11050 The C<isl_ast_build_get_schedule> function returns a (partial)
11051 schedule for the domains elements for which part of the AST still needs to
11052 be generated in the current build.
11053 In particular, the domain elements are mapped to those iterations of the loops
11054 enclosing the current point of the AST generation inside which
11055 the domain elements are executed.
11056 No direct correspondence between
11057 the input schedule and this schedule should be assumed.
11058 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11059 to create a set for C<isl_ast_build_restrict> to intersect
11060 with the current build. In particular, the set passed to
11061 C<isl_ast_build_restrict> can have additional parameters.
11062 The ids of the set dimensions in the space returned by
11063 C<isl_ast_build_get_schedule_space> correspond to the
11064 iterators of the already generated loops.
11065 The user should not rely on the ids of the output dimensions
11066 of the relations in the union relation returned by
11067 C<isl_ast_build_get_schedule> having any particular value.
11069 =head1 Applications
11071 Although C<isl> is mainly meant to be used as a library,
11072 it also contains some basic applications that use some
11073 of the functionality of C<isl>.
11074 For applications that take one or more polytopes or polyhedra
11075 as input, this input may be specified in either the L<isl format>
11076 or the L<PolyLib format>.
11078 =head2 C<isl_polyhedron_sample>
11080 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11081 an integer element of the polyhedron, if there is any.
11082 The first column in the output is the denominator and is always
11083 equal to 1. If the polyhedron contains no integer points,
11084 then a vector of length zero is printed.
11088 C<isl_pip> takes the same input as the C<example> program
11089 from the C<piplib> distribution, i.e., a set of constraints
11090 on the parameters, a line containing only -1 and finally a set
11091 of constraints on a parametric polyhedron.
11092 The coefficients of the parameters appear in the last columns
11093 (but before the final constant column).
11094 The output is the lexicographic minimum of the parametric polyhedron.
11095 As C<isl> currently does not have its own output format, the output
11096 is just a dump of the internal state.
11098 =head2 C<isl_polyhedron_minimize>
11100 C<isl_polyhedron_minimize> computes the minimum of some linear
11101 or affine objective function over the integer points in a polyhedron.
11102 If an affine objective function
11103 is given, then the constant should appear in the last column.
11105 =head2 C<isl_polytope_scan>
11107 Given a polytope, C<isl_polytope_scan> prints
11108 all integer points in the polytope.
11112 Given an C<isl_union_access_info> object as input,
11113 C<isl_flow> prints out the corresponding dependences,
11114 as computed by C<isl_union_access_info_compute_flow>.
11116 =head2 C<isl_codegen>
11118 Given either a schedule tree or a sequence consisting of
11119 a schedule map, a context set and an options relation,
11120 C<isl_codegen> prints out an AST that scans the domain elements
11121 of the schedule in the order of their image(s) taking into account
11122 the constraints in the context set.
11124 =head2 C<isl_schedule>
11126 Given an C<isl_schedule_constraints> object as input,
11127 C<isl_schedule> prints out a schedule that satisfies the given